The generator matrix

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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+118x^71+656x^72+666x^73+758x^74+442x^75+438x^76+208x^77+315x^78+144x^79+134x^80+82x^81+77x^82+24x^83+17x^84+8x^85+4x^87+2x^88+2x^90

The gray image is a linear code over GF(2) with n=600, k=12 and d=284.
This code was found by Heurico 1.16 in 0.328 seconds.