The generator matrix

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

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+70x^70+350x^71+521x^72+466x^73+501x^74+476x^75+439x^76+398x^77+376x^78+318x^79+92x^80+30x^81+23x^82+8x^83+16x^84+2x^85+2x^88+3x^90+2x^94+1x^98+1x^100

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 0.547 seconds.