The generator matrix

 1  0  0  0  1  1  1  1 X^3  1  0  1  1 X^2  X  1  1 X^3+X  X  1  1  X X^3 X^2  1 X^3+X X^2+X  1  1  1  1  1  1  X X^3+X^2 X^3  1  1 X^3+X^2+X  1 X^3+X^2+X X^2+X  1  1  1  1 X^3  1 X^2+X  1  1  1  1  1  1 X^3+X^2+X  1  1 X^2  1 X^3  X  1 X^2+X  1 X^3+X  1 X^3+X^2+X X^3+X^2 X^2+X  1  1 X^3  1  1  1 X^2 X^2  1  1 X^3+X^2+X  1 X^2  0 X^3  X X^3+X^2  1 X^3+X^2+X  1  1  1  1 X^3+X  1  1  1
 0  1  0  0  X X^2+1 X^3  1  1 X^3+X X^3+X X+1 X^3+X+1  1  1 X^3 X+1  X X^3+X^2 X^3+1 X^2+X  1  1  1 X^3+X^2+X+1  1 X^3+X^2+X X^3+X^2+1 X^3+X^2+X X^3+X+1 X^3+X X^2+X+1 X^2  1  0  1 X^2+X X^3+X^2+X  1 X^2+1  1 X^2+X X^2+1 X^3+1 X^3+X^2 X^3+X^2+X  1 X^3 X^2 X^3+X  1 X^3+X+1 X^3+X^2+X+1 X^2+X X^3+X^2+X+1 X^3+X^2+X  X X^3+X^2+1  1 X^3+X+1  1  1 X^3+X^2 X^3+X^2 X+1 X^3 X^2  1  1  1 X+1 X^2  X X+1  0  0 X^3  1 X^3+X+1 X^3+X+1  X X^2+1 X^2+X  1  1  0 X^3  X  1 X^2+X+1 X^2+X X^3+1 X+1 X^3+X^2+X X^3+1 X^3  0
 0  0  1  0  0 X^3 X^3+X^2+1  1 X^3+1 X^3+X^2+X+1  1 X+1 X^3+X  X X^3+X^2+X+1 X^3+X^2+X X^2+1  1  1 X^3+1 X^3+X X^2+1 X^3+X+1  X X^3+X^2  X X^2+X  X X^3+X^2+1  1 X+1 X+1 X^2+X X^3  1 X^3+X^2+X+1 X^2+X+1 X^3+X^2  1 X^2 X^3  1  X X^2+1 X^2 X^2+1 X+1 X^2+1  1  1 X^2+X+1 X^3+X^2+X X^3+1 X^3+X^2+X X^3+X  1 X^3+X X^2+X+1 X^2+1 X^2 X^3+X^2+X+1 X^2 X+1  1 X^3+X^2+X X^2 X^2 X^3+X^2+X  0 X^3+X^2  0 X^2+1  1 X^2+X+1 X+1  1  1 X^2 X+1 X^2+X+1 X^3+X^2 X^3+1 X^3+X X+1 X^3+X  1  1 X^3+1 X+1  1 X^3+X  0 X^3+X^2  0 X^3+X^2+X+1  1  0
 0  0  0  1  1 X^3+X+1 X+1 X^3 X+1 X^3  1 X^2+X+1 X^3+X^2 X^2+1 X^2+X X^3+X^2+X+1 X^3+1 X^2 X^3+1 X^3+X^2+X X^3+X X^3+X^2+X+1 X^3+X X^3+X+1 X^2 X^2  1 X^3+X^2+1 X^3+X+1 X^3+X^2+X+1 X^3+X^2+X X^3+X^2+X X^3+1 X^2+1 X^2+1 X^3+X+1 X^3+1  X  X  1 X^2 X^2+X X^3 X^2+X+1  X  0 X^3+1 X^2+X X^3+X^2+X+1 X^3+1 X+1 X^3+X^2 X^3+X X+1 X^3+X^2+X+1 X+1 X^3+X^2 X^3+X^2  0 X^2+1 X^3 X^3+X^2+X  0  X X^2+1  1 X^3 X^3+X+1 X^3+X^2 X^3+X^2+X+1 X^2+X  X X+1 X^3+X^2 X+1  0 X^3+X^2+X X+1  1 X^2+X+1  1 X^3  1 X^3+X^2+X X^3+X  0 X^2  X  1 X^3 X^2+X X^2+X X^3+X^2+X+1  1  X X^2+X X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3

generates a code of length 97 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+117x^88+962x^89+2400x^90+4010x^91+5974x^92+8106x^93+10421x^94+12430x^95+13891x^96+15192x^97+13594x^98+12680x^99+10394x^100+8028x^101+5686x^102+3200x^103+1789x^104+1120x^105+598x^106+240x^107+116x^108+62x^109+33x^110+14x^111+6x^112+2x^113+4x^114+2x^115

The gray image is a linear code over GF(2) with n=776, k=17 and d=352.
This code was found by Heurico 1.16 in 235 seconds.