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

generates a code of length 76 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+99x^72+208x^73+192x^74+464x^75+166x^76+608x^77+92x^78+48x^79+45x^80+48x^81+28x^82+32x^83+16x^84+1x^144

The gray image is a linear code over GF(2) with n=608, k=11 and d=288.
This code was found by Heurico 1.16 in 0.547 seconds.