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

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+226x^72+576x^74+216x^76+4x^80+1x^144

The gray image is a linear code over GF(2) with n=592, k=10 and d=288.
This code was found by Heurico 1.16 in 0.719 seconds.