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  1  1 X^3  1  1  1  1  X  X  1  1  1  1  1  X  0  X  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2+X  0 X^3+X^2 X^3+X X^3 X^2+X X^3+X^2  X  0 X^2+X X^2  X X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3 X^3+X^2+X X^2  X X^2  X X^2  X X^3 X^3+X^2+X X^3 X^3+X^2+X X^2  X X^3 X^3+X^2+X X^2 X^3+X^2  X X^2+X X^3+X^2 X^3+X  X X^3+X X^2 X^3 X^3 X^3 X^2+X X^3 X^2+X X^2+X X^3  0 X^3  0 X^2+X X^2+X X^3+X^2+X X^2+X  X X^3+X^2+X  0
 0  0 X^3+X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3 X^3  0  0 X^3 X^3 X^2 X^3+X^2 X^3  0  0  0 X^2 X^2 X^3  0 X^2 X^2 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3  0 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2  0  0 X^3 X^2  0
 0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  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+36x^70+62x^71+218x^72+248x^73+347x^74+368x^75+348x^76+168x^77+60x^78+18x^79+113x^80+28x^81+16x^82+8x^84+4x^85+4x^86+1x^138

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 0.672 seconds.