The generator matrix

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

generates a code of length 74 over Z2[X]/(X^4) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+308x^67+1462x^68+2756x^69+4266x^70+5314x^71+7053x^72+7734x^73+8638x^74+7590x^75+6544x^76+5218x^77+4059x^78+2284x^79+1321x^80+558x^81+244x^82+86x^83+54x^84+22x^85+17x^86+2x^87+5x^88

The gray image is a linear code over GF(2) with n=592, k=16 and d=268.
This code was found by Heurico 1.16 in 41.7 seconds.