The generator matrix

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

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+107x^88+108x^89+315x^90+188x^91+394x^92+220x^93+353x^94+252x^95+364x^96+244x^97+333x^98+244x^99+305x^100+180x^101+216x^102+84x^103+78x^104+16x^105+31x^106+16x^108+19x^110+8x^112+9x^114+5x^116+4x^118+1x^128+1x^136

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 2.1 seconds.