The generator matrix

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

generates a code of length 80 over Z2[X]/(X^4) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+148x^75+330x^76+504x^77+492x^78+416x^79+462x^80+424x^81+433x^82+376x^83+272x^84+116x^85+46x^86+46x^87+7x^88+12x^89+1x^90+2x^91+2x^98+2x^99+2x^103+2x^106

The gray image is a linear code over GF(2) with n=640, k=12 and d=300.
This code was found by Heurico 1.16 in 0.765 seconds.