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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+124x^71+144x^72+288x^73+336x^74+384x^75+312x^76+240x^77+47x^78+60x^79+35x^80+48x^81+16x^82+8x^83+4x^84+1x^142

The gray image is a linear code over GF(2) with n=600, k=11 and d=284.
This code was found by Heurico 1.16 in 0.547 seconds.