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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+80x^73+141x^74+8x^75+10x^76+4x^77+2x^78+5x^80+4x^89+1x^90

The gray image is a linear code over GF(2) with n=592, k=8 and d=292.
This code was found by Heurico 1.16 in 9.37 seconds.