The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X^2  1  0  1  X  1  1  0  1  1 X^2+X  1  1  X X^2+X X^2+X X^2  1  0 X^2+X X^2  1  1  1  1 X^2  1  X X^2+X  0  1 X^2  1  1  X  1  1  1  1  1 X^2 X^2+X  1  0  1  0  1  1  0  1  1 X^2+X  1  0  1 X^2+X X^2 X^2+X X^2+X  1 X^2  1  X  1  1  1  0  1  X  1  1  1  X  1  1  1  1  1  1  1  1  1 X^2  1
 0  1  0  0  X  X X^2+X  0  1 X^2+1  1  1  1 X^2+X+1  1 X^2+X X^2 X^2+X  0 X+1  1 X^2+1 X^2  1  0  1 X^2+X X^2+1  1  1  1 X^2+X X+1  0 X+1  0 X^2+1  X  1 X^2+X X^2+1  1  1  0  1 X^2  X X+1  X X+1  1 X^2+X X^2+1  1 X+1  1  1 X^2+X+1  1 X^2 X+1 X^2+X X^2+X  1 X^2+X  1 X^2  1  1  0  X X^2+X+1  1 X^2+X+1 X^2 X^2 X^2  0  X X+1  1  1  0 X^2+1 X^2+X  X X+1 X+1 X^2 X^2  0 X^2  1 X^2
 0  0  1  0  X X^2+X+1 X^2+X+1  1 X+1 X+1 X^2  0 X+1  X  1  X  1  0 X^2+1 X^2  0 X^2+1  X X^2+X  1  1  1 X^2 X^2 X+1  X X^2+1 X^2+X+1 X^2+1 X^2  1  1  X X+1  1 X+1 X^2+X  X X^2+X  1 X^2+X+1 X^2 X^2+X  X X^2+X+1 X+1  1  0 X^2+X X+1  0 X^2  1 X^2+1  1 X^2+1 X^2+X X^2+X X^2 X+1  0  1 X^2 X^2+1  1  0  1 X^2 X^2 X^2 X^2+X+1 X^2+X  1  1 X^2+1 X^2+1  0  1  X  X  0 X^2+X+1  0  0  1 X^2+X X^2+X+1 X^2+X+1 X^2
 0  0  0  1 X+1 X^2+X+1  X  1  X X^2+X+1 X^2+X+1 X^2+X X^2+X  1  1 X^2+X X^2  1 X^2+1  X X^2+1 X^2+X X^2+X+1  0 X^2 X^2+X X+1 X^2+1 X^2+1 X^2+X+1  0 X^2+1 X^2+1 X^2+X+1 X+1 X^2+X+1 X^2+X+1  1 X^2+1  0  0 X^2+X X^2+X X^2+X+1 X^2 X^2+X  0 X^2+1  1 X^2 X+1 X^2+X X^2+X X^2 X^2+X+1 X^2  0 X^2+X+1  X  1 X^2  1  0 X^2+1 X^2+X  0  X X+1 X^2+X+1 X^2+1  1  1 X^2+X X^2  X  0  1 X^2+X  0  0 X^2+X+1 X^2  X  0 X^2+X  0  1 X^2+1 X^2+1 X^2+X  X X^2+X X+1 X^2
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2

generates a code of length 94 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+112x^86+388x^87+425x^88+624x^89+644x^90+674x^91+592x^92+688x^93+592x^94+616x^95+487x^96+454x^97+367x^98+350x^99+300x^100+290x^101+184x^102+148x^103+66x^104+74x^105+43x^106+30x^107+14x^108+14x^109+10x^110+3x^112+2x^115

The gray image is a linear code over GF(2) with n=376, k=13 and d=172.
This code was found by Heurico 1.16 in 5.1 seconds.