The generator matrix

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

generates a code of length 75 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+562x^72+594x^74+389x^76+328x^78+147x^80+22x^82+2x^84+1x^88+1x^92+1x^120

The gray image is a linear code over GF(2) with n=600, k=11 and d=288.
This code was found by Heurico 1.16 in 59.9 seconds.