The generator matrix

 1  0  1  1  1 X^2+X X^2  1  1  1  1  X  1  1  0  0  1  1  1 X^2+X  1  1  X  1  1  0  1  X  1  1  1 X^2+X  1  1 X^2  1  1 X^2+X  1  X  1  1  1  X  1  0  0  1  0  1 X^2 X^2  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1 X^2+X  1  1  1  1  1 X^2  1 X^2  1  1  1  1  1  1 X^2  0  X  1  1  1  1  1 X^2 X^2+X X^2  1  1  1  X
 0  1  1  0  1  1  1 X^2 X+1 X^2+1  X  1 X^2+X X^2+X+1  1  1  X  1  1  1  0 X+1  1 X^2+X X+1  1 X^2  1 X^2+X+1  0 X^2+X  1 X^2+1 X+1  1 X^2  X  1  1  1  0 X^2+X  1  1 X^2+X+1  1  1 X^2+X  1  0  1  1  1 X^2+1 X^2+1  0  X X^2+X+1  0  1 X^2+X+1 X^2  1 X^2  X X^2+1  X  1 X+1  0 X^2+X X^2+X+1 X^2+1  1 X^2  1 X^2+X+1  0 X^2+X+1  X X+1 X^2+1  1  1  1 X^2+X+1 X^2+X  1 X^2+X+1 X^2+X+1  1  1  0  1 X^2+X X^2+X+1 X^2
 0  0  X  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  X X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2+X  X  X X^2+X  X X^2+X  X  X  X X^2+X X^2+X  X X^2+X  X X^2  X  X  X X^2+X  X X^2+X X^2  0 X^2 X^2+X  0 X^2 X^2 X^2+X  0  X X^2 X^2 X^2+X  X X^2 X^2+X X^2+X  X  X X^2+X  X X^2+X  X X^2+X  0 X^2+X X^2  0  X X^2  X  0  0  0 X^2+X  0 X^2  X X^2 X^2
 0  0  0  X  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2+X  X  X X^2+X X^2+X X^2+X  X X^2+X  X  X X^2+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^2  0 X^2+X X^2+X X^2+X X^2+X X^2 X^2  0  X  X  X  0  0  0  0  0  X X^2  0  0 X^2+X X^2 X^2+X X^2  X  0  X  X X^2  0 X^2  X  X  X X^2 X^2+X  0 X^2  X X^2+X X^2  0  0  X  X X^2 X^2 X^2+X  X X^2  0 X^2+X X^2+X X^2  0 X^2  0 X^2+X  X  0 X^2+X
 0  0  0  0  X  0 X^2+X X^2+X X^2  0  X X^2+X X^2 X^2+X  X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2 X^2 X^2+X  0  X  0 X^2+X  X  0  X  X  0 X^2+X X^2 X^2+X X^2+X X^2 X^2  X X^2 X^2 X^2  X X^2+X  0 X^2+X X^2 X^2+X  0  X X^2 X^2  0  0 X^2  X X^2+X  0 X^2 X^2  0 X^2  X X^2+X X^2+X  X X^2  X  0 X^2  X X^2 X^2+X  0 X^2+X X^2  X X^2+X X^2+X  0  X  0  0  X  0  0 X^2  0  X  X X^2+X X^2 X^2+X
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  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 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  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+195x^88+108x^89+378x^90+308x^91+665x^92+396x^93+742x^94+456x^95+704x^96+516x^97+780x^98+480x^99+577x^100+420x^101+462x^102+280x^103+297x^104+96x^105+116x^106+12x^107+71x^108+58x^110+38x^112+20x^114+6x^116+2x^118+4x^120+2x^122+1x^128+1x^132

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 7.26 seconds.