The generator matrix

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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+51x^72+170x^73+112x^74+128x^75+10x^76+10x^77+14x^78+8x^79+2x^80+2x^81+2x^85+2x^86

The gray image is a linear code over GF(2) with n=592, k=9 and d=288.
This code was found by Heurico 1.16 in 0.25 seconds.