The generator matrix

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

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+366x^71+571x^72+498x^73+435x^74+560x^75+386x^76+464x^77+444x^78+198x^79+63x^80+54x^81+15x^82+4x^83+2x^84+12x^85+8x^87+12x^89+1x^90+1x^98+1x^104

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 0.64 seconds.