The generator matrix

 1  0  0  0  1  1  1  1  1 X^3+X X^3+X^2+X X^3+X^2+X  1  1 X^2+X X^3+X^2+X  1  X  X X^3+X^2+X X^3+X  1  1  1  1 X^3+X^2  1  1 X^2+X  1 X^3+X^2+X X^3+X^2+X  1  1  X  1  1 X^3+X^2+X  0  1 X^3+X X^3  1 X^3+X^2  1  1  1 X^2  1 X^3+X  0  1  1  1  0 X^2  1 X^3+X^2  1  X  X X^2+X  1 X^3+X^2  1 X^3+X^2+X  1  1  1  1  1  0  1 X^2+X  1  1  1  1  1 X^3+X  0  1
 0  1  0  0  0 X^3+X^2+1 X^3+X+1 X^2+1 X+1 X^3  1  1 X^3+X^2 X^2  1  0 X^3+X^2+X+1  1  1  1 X^2+X X^2+X+1  1  X X^3+X^2+1  1 X^3+X  X X^3+X^2+X X^3+X^2 X^3+X^2+X  1 X^3+X^2 X^3+X X^3+X^2 X^2+X+1 X^3+X^2  1  1 X^2  1 X^3+X^2  1 X^3 X+1 X^3+1 X^3+1 X^3+X^2  X  1  1 X^2+X+1 X^2 X^3+1  1  X X^2+X  1 X^2+X  1  1  1 X^2+X+1  1 X^2+1  1 X^3+1 X^3+X^2+X+1  0 X^3+1  X  1 X^2  X X^3+X+1  0 X^2 X^3+X+1 X^2+1  1  1  X
 0  0  1  0 X^2 X^3 X^3+X^2 X^2+1 X^3+X^2+X+1  1 X^3 X+1 X^3+X^2+1 X+1 X^3+1 X^3+X X^3+1  1 X+1  0  1 X^3+X^2 X^3 X^3+X X^2+X+1 X^3+X X^3+X^2+1 X^3+1  1 X^2+X X^2+X X^3+X^2+X X^2+X+1 X^2+X  1 X+1 X+1  X X^3+X^2+X+1 X^2+X X+1  1 X^3+X^2+X  1 X^3+X^2+X X^3+X+1  0 X^3+X X^2+1 X^2 X^3+X^2+1 X^3+X^2+1 X^2 X^3+X^2+X+1 X+1 X^3+X^2+X X^2+X X^3 X^3 X^3+X+1 X^3+X^2+1  0 X^3+X^2+1 X^2  X X^2+X+1 X^3+X^2 X^3+1  X X^3+X^2+1  0  1  1  1 X^2+X X^3+X^2 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+X+1  1 X^2+1 X^2+X
 0  0  0  1 X^2+X+1 X^3+X^2+X+1 X^3 X^3 X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+1 X+1 X^2+1  X X^2  1  X X^3+X  1 X+1 X^3+X^2+X+1 X^2+X X^2+1 X^3+X^2 X^3+X^2+1  X X^2 X^3+X^2+X+1 X^2+X  1  1 X^2+X X^2+X+1 X^2+X X^2+X+1 X^3  0 X^2+1 X^3+X^2 X^3+X+1 X^2 X^2+X+1  0 X^3+X^2+X  1 X^2 X^3+X^2  1  X X^3+X^2+X  1 X^3+X+1 X^3+1  1 X+1  1 X^3+X^2+X+1 X^3+X X^3+X^2 X^3+X^2+X X^3+X  0 X^3+X+1 X^3+X+1 X^3+X^2+1 X^3+X^2+X X^3 X^3+X^2+1  1 X^3+X^2+X  1 X^3+X^2+X+1 X^2+X X^3 X^3+X^2 X^3+X^2  0 X^2+1  X  1 X^2+1 X^3
 0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0

generates a code of length 82 over Z2[X]/(X^4) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+372x^74+1654x^75+3304x^76+5706x^77+7532x^78+11048x^79+12753x^80+15626x^81+15038x^82+16228x^83+13156x^84+10742x^85+7407x^86+5278x^87+2661x^88+1286x^89+552x^90+418x^91+145x^92+88x^93+35x^94+14x^95+7x^96+8x^97+8x^98+4x^100+1x^108

The gray image is a linear code over GF(2) with n=656, k=17 and d=296.
This code was found by Heurico 1.16 in 192 seconds.