The generator matrix

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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+87x^86+300x^87+607x^88+904x^89+1305x^90+1460x^91+1794x^92+1868x^93+2458x^94+2132x^95+2613x^96+2206x^97+2546x^98+2268x^99+2413x^100+1696x^101+1561x^102+1288x^103+1109x^104+676x^105+599x^106+368x^107+204x^108+116x^109+70x^110+40x^111+12x^112+22x^113+14x^114+16x^115+13x^116+2x^120

The gray image is a linear code over GF(2) with n=388, k=15 and d=172.
This code was found by Heurico 1.16 in 69.2 seconds.