The generator matrix

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

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+323x^72+360x^73+368x^74+128x^75+345x^76+224x^77+168x^78+32x^79+36x^80+24x^81+24x^82+5x^84+8x^88+2x^108

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 0.375 seconds.