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

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+334x^70+64x^71+543x^72+224x^73+760x^74+432x^75+714x^76+256x^77+338x^78+48x^79+212x^80+126x^82+33x^84+8x^86+2x^90+1x^124

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 33.1 seconds.