The generator matrix

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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+80x^70+790x^71+887x^72+1210x^73+930x^74+1228x^75+718x^76+780x^77+417x^78+462x^79+248x^80+246x^81+85x^82+72x^83+18x^84+12x^85+6x^86+1x^90+1x^94

The gray image is a linear code over GF(2) with n=600, k=13 and d=280.
This code was found by Heurico 1.16 in 9.75 seconds.