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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+55x^68+84x^70+241x^72+1362x^74+192x^76+36x^78+28x^80+18x^82+24x^84+4x^86+2x^88+1x^140

The gray image is a linear code over GF(2) with n=592, k=11 and d=272.
This code was found by Heurico 1.16 in 0.515 seconds.