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

generates a code of length 73 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+19x^68+13x^70+64x^71+31x^72+768x^73+31x^74+64x^75+13x^76+18x^78+1x^82+1x^142

The gray image is a linear code over GF(2) with n=584, k=10 and d=272.
This code was found by Heurico 1.16 in 0.407 seconds.