The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 0 1 1 X 1 1 X 1 1 1 1 X 1 1 1 1 0 1 1 1 X 1 1 0 0 X 1
0 X 0 0 0 X^2 0 X^2 0 X X X^2+X X X^2+X X^2+X X X^2 X X^2+X X 0 0 X X^2 X 0 X X^2+X X^2 0 X^2 X^2+X X X^2+X X^2+X X^2+X 0 0 X^2 0 X^2 X^2 X^2+X X X^2+X X^2+X 0 0 X^2+X X^2+X X^2+X X^2 X X^2+X 0 X^2+X 0 X^2 X^2 X^2 X^2 0 X^2 0 X X^2+X X^2 X^2+X 0 X^2 X X 0 X^2 X^2 X^2+X X^2+X X X X 0 X^2 X^2+X X^2 0 0 0 0 0 X^2+X 0
0 0 X 0 0 X^2 X X X X^2+X X X^2 X X^2+X 0 0 0 X^2 X X^2+X 0 X^2+X X^2 X^2+X X X X^2+X 0 X^2 X 0 X^2 X 0 0 X X^2 X^2+X X 0 0 X^2 X^2 X^2+X X X^2+X X X X^2+X 0 X X^2+X X X^2 X^2+X X^2+X X^2 X^2+X 0 X^2+X 0 0 X^2 0 X^2 0 X X X^2 0 X^2+X X^2 X^2 X X^2+X 0 X X^2+X 0 X X X^2+X X X X^2+X X^2 X^2+X 0 0 X^2+X X^2
0 0 0 X 0 X X X^2+X X^2 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2+X 0 X X^2 X^2 X^2 X^2+X X 0 0 0 X^2+X X X^2 X 0 X^2+X 0 0 X X X^2 X 0 X^2+X X^2+X 0 X X^2+X X^2 X^2 X 0 X^2 X^2+X X X^2+X X 0 X^2 X^2 X^2+X X^2 X^2+X X X X X^2+X X 0 0 0 X 0 X X^2+X X 0 X X^2 X^2+X X^2+X X X X X X X^2+X X X X^2+X X^2+X
0 0 0 0 X X X^2 X X^2+X X X 0 0 X^2 X X 0 X^2+X X^2+X X X^2 0 X 0 X^2 X^2+X 0 X^2 X^2+X X^2+X X X^2 0 X^2 0 0 0 X^2 X^2 X X^2+X X^2 X X^2+X X X^2+X X^2+X X X^2 X^2 0 X^2+X X X^2+X X^2 0 X^2 X^2 X X X^2 X^2 X X^2+X X 0 0 X X^2 X^2 0 X X^2+X X^2+X X X X^2+X X^2+X X^2+X 0 X X^2+X X X X^2+X X^2+X 0 X^2+X 0 0 X^2
generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+226x^84+484x^88+288x^90+633x^92+96x^94+172x^96+100x^100+36x^104+9x^108+2x^112+1x^160
The gray image is a linear code over GF(2) with n=364, k=11 and d=168.
This code was found by Heurico 1.16 in 99.8 seconds.