The generator matrix

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

generates a code of length 92 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+278x^86+336x^87+444x^88+384x^89+374x^90+344x^91+383x^92+276x^93+283x^94+124x^95+190x^96+128x^97+137x^98+72x^99+85x^100+56x^101+71x^102+44x^103+33x^104+16x^105+25x^106+8x^107+4x^109

The gray image is a linear code over GF(2) with n=368, k=12 and d=172.
This code was found by Heurico 1.11 in 0.891 seconds.