The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+18x^88+68x^89+236x^90+110x^91+418x^92+162x^93+475x^94+154x^95+466x^96+120x^97+437x^98+142x^99+410x^100+94x^101+313x^102+72x^103+186x^104+42x^105+46x^106+26x^107+26x^108+16x^109+18x^110+6x^111+8x^112+10x^113+5x^114+2x^115+2x^116+1x^118+4x^122+1x^126+1x^128

The gray image is a linear code over GF(2) with n=388, k=12 and d=176.
This code was found by Heurico 1.16 in 2.06 seconds.