The generator matrix

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

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+244x^88+432x^89+736x^90+898x^91+981x^92+1016x^93+1286x^94+1184x^95+1340x^96+1068x^97+1140x^98+992x^99+995x^100+832x^101+927x^102+578x^103+588x^104+330x^105+316x^106+238x^107+92x^108+78x^109+41x^110+22x^111+11x^112+2x^113+2x^114+4x^115+2x^116+2x^117+4x^119+2x^120

The gray image is a linear code over GF(2) with n=388, k=14 and d=176.
This code was found by Heurico 1.13 in 6.33 seconds.