The generator matrix

 1  0  1  1  1 X^2+X  1 X^3+X^2  1  1  1 X^3+X  1  1 X^3  1 X^3+X^2+X  1  1  1 X^2  1  1  X  1  1  0  1 X^2+X  1  1  0 X^2+X  1  1  1  1  1  1  1 X^2  X  1  1 X^2  X  X  1  X  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1  1 X^2  1  1  1 X^2  1  1  1 X^3+X^2+X  X
 0  1 X+1 X^2+X X^2+1  1 X^3+1  1 X^3+X^2 X+1 X^3+X  1 X^3+X^2+X+1 X^3  1 X^3+X^2+X  1 X^3+X^2+1 X^2+X+1 X^2  1  X  1  1  0 X+1  1 X^2+X  1 X^3+X^2+X+1 X^3+X^2+1  1  1 X^3+X+1  0  X  1 X^3+X^2+X+1 X^2 X^2+X  1  1 X^2+1 X^2  1 X^3+X X^3+X  X  1 X^3+1 X^3+1 X^3+X+1 X^3+X^2+1 X+1  1 X^2+1 X+1 X^2+X+1  1 X^3+X^2+1 X^2 X^3+X+1 X^2+X+1 X^3+1 X^2+1  X X^3+X+1 X^3 X^3+X^2+X+1 X^3+X^2 X^3+X^2 X+1 X^3+X^2+X  1 X^2
 0  0 X^2  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^3  0  0  0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3+X^2 X^3  0  0 X^3 X^2 X^3 X^3+X^2  0 X^2 X^2 X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2  0 X^2 X^3 X^3
 0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 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+99x^70+280x^71+615x^72+416x^73+641x^74+352x^75+464x^76+360x^77+391x^78+184x^79+151x^80+48x^81+37x^82+16x^83+9x^84+8x^85+14x^86+4x^88+2x^90+2x^92+1x^100+1x^104

The gray image is a linear code over GF(2) with n=600, k=12 and d=280.
This code was found by Heurico 1.16 in 0.656 seconds.