The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+369x^62+392x^63+688x^64+408x^65+596x^66+376x^67+548x^68+296x^69+254x^70+64x^71+52x^72+28x^74+20x^76+1x^78+1x^80+2x^88

The gray image is a linear code over GF(2) with n=528, k=12 and d=248.
This code was found by Heurico 1.16 in 0.843 seconds.