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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1 X^2  1  1  1 X^2  1  1 X^2  1  X  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^2 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3 X^2 X^3 X^3+X^2 X^2 X^2 X^2 X^3 X^3 X^3 X^2  0 X^2  0 X^2 X^3+X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^2 X^2 X^3+X^2 X^3  0  0 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^2 X^2  0 X^3  0 X^2 X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^2  0  0 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 X^3 X^3+X^2 X^2  0 X^3  0 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3 X^2 X^3 X^2 X^2  0 X^3 X^2 X^3 X^2 X^2  0 X^3 X^3  0 X^2 X^3+X^2 X^3+X^2 X^3 X^2  0 X^2 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3  0 X^3  0 X^3
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^2  0 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3 X^3 X^2  0 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^3 X^3+X^2  0 X^3+X^2  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3 X^3  0 X^3  0 X^2 X^2  0 X^3 X^3  0 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 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^2
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 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+134x^70+145x^72+96x^73+532x^74+320x^75+456x^76+96x^77+166x^78+37x^80+50x^82+12x^86+2x^90+1x^136

The gray image is a linear code over GF(2) with n=600, k=11 and d=280.
This code was found by Heurico 1.16 in 109 seconds.