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  0  1  1  1  1  X  1  1  1  1  1  0  1  1  1 X^3+X^2  X  1 X^3  1  1  X  1  1  1  X X^2  1  1  1 X^3  0  1  X  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X  0 X^2+X X^3 X^2+X X^3+X X^2 X^2  X  0 X^2+X X^2 X^3+X X^3 X^3+X X^3 X^3+X X^3+X X^3+X^2 X^3+X  0  0  X X^2+X X^2 X^2  X  0 X^3+X^2+X  X X^2+X  X  0 X^3  0 X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2+X X^2+X X^3 X^2+X  X X^2 X^2+X X^2+X  X X^3+X^2+X X^3+X^2+X  X  X  X X^2 X^2+X  0 X^2  0  X X^3+X^2 X^3 X^2  0  X X^3+X^2 X^3+X  X X^3
 0  0 X^3+X^2  0 X^2  0 X^3  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2  0 X^3  0  0 X^2 X^2 X^2 X^2 X^3  0 X^3+X^2  0 X^2 X^2 X^3 X^3 X^2  0 X^3 X^2  0 X^3 X^3 X^2 X^3 X^2 X^2 X^2  0 X^3 X^3 X^3+X^2  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^2  0
 0  0  0 X^3+X^2  0 X^3 X^3 X^2 X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^3  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^3+X^2 X^2  0  0  0 X^2 X^2  0 X^3+X^2 X^3 X^2
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  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  0  0 X^3  0  0 X^3 X^3 X^3  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+113x^68+136x^69+256x^70+232x^71+506x^72+544x^73+652x^74+548x^75+437x^76+204x^77+188x^78+80x^79+91x^80+40x^81+30x^82+4x^83+17x^84+4x^85+8x^86+2x^88+2x^90+1x^124

The gray image is a linear code over GF(2) with n=592, k=12 and d=272.
This code was found by Heurico 1.16 in 0.922 seconds.