The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+142x^67+574x^68+1156x^69+1751x^70+2634x^71+3619x^72+5278x^73+6192x^74+7736x^75+8536x^76+10530x^77+10685x^78+11998x^79+11110x^80+11260x^81+9353x^82+8324x^83+6235x^84+4880x^85+3212x^86+2374x^87+1498x^88+850x^89+529x^90+300x^91+161x^92+82x^93+20x^94+26x^95+8x^96+12x^97+2x^98+2x^99+2x^100

The gray image is a linear code over GF(2) with n=316, k=17 and d=134.
This code was found by Heurico 1.13 in 255 seconds.