The generator matrix

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

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+238x^62+280x^63+440x^64+312x^65+676x^66+400x^67+561x^68+272x^69+393x^70+216x^71+163x^72+56x^73+68x^74+19x^76+1x^118

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 1.31 seconds.