The generator matrix

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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+102x^69+184x^70+244x^71+262x^72+596x^73+357x^74+710x^75+308x^76+580x^77+260x^78+220x^79+125x^80+86x^81+13x^82+6x^83+4x^84+10x^85+15x^86+4x^87+3x^88+2x^89+2x^90+1x^94+1x^120

The gray image is a linear code over GF(2) with n=600, k=12 and d=276.
This code was found by Heurico 1.16 in 85.3 seconds.