The generator matrix

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

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+75x^64+480x^65+955x^66+1758x^67+2461x^68+3780x^69+4734x^70+6474x^71+7510x^72+9332x^73+10077x^74+11736x^75+11469x^76+11994x^77+10525x^78+9822x^79+8016x^80+6620x^81+4438x^82+3532x^83+2094x^84+1408x^85+789x^86+424x^87+225x^88+168x^89+94x^90+46x^91+20x^92+10x^93+4x^94+1x^96

The gray image is a linear code over GF(2) with n=304, k=17 and d=128.
This code was found by Heurico 1.13 in 242 seconds.