The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+156x^66+432x^67+1017x^68+1764x^69+2498x^70+3914x^71+5154x^72+6258x^73+7600x^74+8932x^75+10521x^76+11262x^77+11609x^78+11380x^79+10542x^80+9450x^81+7972x^82+6688x^83+4848x^84+3418x^85+2382x^86+1334x^87+885x^88+516x^89+244x^90+132x^91+78x^92+36x^93+19x^94+20x^95+10x^96

The gray image is a linear code over GF(2) with n=312, k=17 and d=132.
This code was found by Heurico 1.13 in 251 seconds.