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

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+30x^72+180x^73+158x^74+288x^75+160x^76+168x^77+32x^78+1x^80+4x^81+1x^82+1x^130

The gray image is a linear code over GF(2) with n=600, k=10 and d=288.
This code was found by Heurico 1.16 in 0.281 seconds.