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

generates a code of length 83 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+358x^75+1751x^76+3036x^77+5898x^78+7914x^79+11746x^80+11662x^81+16276x^82+14584x^83+15387x^84+12976x^85+11287x^86+7122x^87+5768x^88+2462x^89+1617x^90+678x^91+336x^92+114x^93+57x^94+16x^95+19x^96+4x^97+2x^101+1x^122

The gray image is a linear code over GF(2) with n=664, k=17 and d=300.
This code was found by Heurico 1.16 in 189 seconds.