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

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+128x^71+122x^72+160x^73+679x^74+268x^75+240x^76+200x^77+72x^78+56x^79+21x^80+48x^81+16x^82+28x^83+8x^85+1x^138

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 39.6 seconds.