The generator matrix

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

generates a code of length 96 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+31x^88+212x^89+207x^90+376x^91+248x^92+358x^93+235x^94+384x^95+178x^96+394x^97+218x^98+316x^99+204x^100+268x^101+110x^102+174x^103+57x^104+36x^105+20x^106+16x^107+6x^108+6x^109+2x^110+8x^111+6x^112+6x^113+6x^114+4x^115+2x^116+2x^119+2x^120+1x^122+1x^126+1x^128

The gray image is a linear code over GF(2) with n=384, k=12 and d=176.
This code was found by Heurico 1.16 in 1.83 seconds.