The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+60x^75+365x^76+860x^77+1460x^78+2188x^79+2928x^80+4004x^81+4921x^82+6252x^83+7744x^84+8744x^85+9921x^86+10674x^87+10701x^88+10378x^89+10147x^90+9200x^91+7904x^92+6486x^93+4959x^94+3844x^95+2716x^96+1738x^97+1172x^98+744x^99+415x^100+270x^101+104x^102+62x^103+58x^104+32x^105+20x^106

The gray image is a linear code over GF(2) with n=352, k=17 and d=150.
This code was found by Heurico 1.13 in 287 seconds.