The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  X  1 X^2  1  1 X^2  X  1  1 X^2  1  1  1  X  0  1  X  1  1  1  1 X^2+X  0  0  1  1  1  0 X^2+X  1  1  1  1 X^2  1  1  X X^2 X^2+X  1  X  1  1  0 X^2+X  1  1  X  1  1  1  1  1 X^2+X  X  1  1  1  1 X^2+X  1  1  X  X  X  0  1  1  X  1  X  0  1  1  1  1  1  1  1  1  1  1  0  X X^2+X  1
 0  1  0  0  1 X^2+X+1  1 X^2  0 X^2 X^2+X+1  1  1  1 X^2 X+1  1  X X^2 X^2+1  1 X^2+X  1 X+1  X  1 X^2+X  1  X  1 X+1 X^2+X  1  1  0  X  1 X^2 X^2+X  1 X^2+1 X^2+X+1  X X^2+1  1  1 X^2  1  1  1 X^2+1 X^2 X+1  1 X^2+X  1 X^2+X X+1  1  0  0  0 X^2+X+1 X^2  1  1  0 X^2+X+1  0 X^2+X+1 X^2+X X^2+X+1  X  X X^2+X X^2+X X^2+X  1 X^2+X  1 X^2  1  1 X+1 X^2+1  X X^2 X+1 X^2+X X^2 X^2  0 X^2+1  0  1  1  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  0  1  0  1 X^2+X  1  1 X^2+X X^2+X+1 X^2+X X^2+X  1  1 X^2+X X^2+1 X+1 X^2  0 X+1 X^2+X+1  X X^2+X+1  1  0  X  X  1 X^2+1 X^2+1 X^2+X X^2+1  0 X^2 X+1 X^2+X+1 X^2+1 X^2 X+1  1  1 X+1 X^2  1 X^2 X^2+X+1 X^2+X+1 X+1 X+1  1 X^2+X  X  0 X^2 X^2  1 X^2+X+1  X  0  1 X+1  X  1  1  1  1 X^2+X X^2+X  1 X^2+X  1 X^2+X+1  0 X^2+X+1 X^2+X+1 X^2+X X^2+X  0 X+1  1 X^2+X+1 X^2+1  1  1 X^2  0
 0  0  0  X  X X^2+X X^2 X^2+X  0  0  X X^2 X^2+X  0  X  X  0  0 X^2 X^2  X  X  X X^2  X  X X^2  X  0  0  0 X^2  X  0  X X^2+X X^2+X  X X^2+X  X X^2+X  X X^2  0 X^2+X  0  0  X X^2  0 X^2+X  X X^2+X X^2+X  0  X X^2+X X^2 X^2 X^2  X  0  0  X X^2+X  0 X^2 X^2+X  0  X  X  0 X^2 X^2 X^2+X  X  0 X^2 X^2+X  0  0 X^2+X X^2  X X^2 X^2  X X^2+X  X  X X^2+X  X  0 X^2+X X^2+X X^2  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  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+69x^88+176x^89+404x^90+366x^91+643x^92+510x^93+618x^94+600x^95+712x^96+560x^97+633x^98+430x^99+559x^100+370x^101+440x^102+262x^103+239x^104+170x^105+160x^106+88x^107+55x^108+32x^109+38x^110+10x^111+23x^112+6x^113+7x^114+4x^115+3x^116+4x^118

The gray image is a linear code over GF(2) with n=388, k=13 and d=176.
This code was found by Heurico 1.16 in 5.47 seconds.