The generator matrix

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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+77x^62+304x^63+472x^64+388x^65+513x^66+672x^67+503x^68+432x^69+341x^70+228x^71+105x^72+12x^73+27x^74+4x^75+2x^76+1x^78+4x^79+2x^80+4x^83+2x^84+1x^92+1x^94

The gray image is a linear code over GF(2) with n=536, k=12 and d=248.
This code was found by Heurico 1.16 in 0.485 seconds.