The generator matrix

 1  0  0  1  1  1 X^3  1  1  0 X^2  1  1 X^3+X  X  1  1  1  1 X^3 X^3+X  1 X^2+X  1 X^2  1  1 X^3+X X^2+X  1  1  0  1 X^3+X^2  1  1 X^2  1  1  X X^3+X X^3+X^2 X^3+X^2+X  X X^2+X  1  1 X^2 X^2+X  1  1 X^3+X^2  1 X^3  1 X^2  1  1 X^2+X  1  1  1  1  1  1  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X  X  1 X^3+X+1 X+1  1  1 X^3+X^2+1  0 X^2+X+1 X^2  1  X  1  1  0  1 X^2+X+1 X^3+X^2  1  0 X^3+X^2+X+1 X^2+X  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+1 X^3+X  1  1 X^2  1  1  1  1 X^3+X+1 X^3+X X^2+X X+1 X^3+X^2+1 X^3 X^3+X^2+X  1 X^2+X  1 X^3+X^2 X^2+X  1 X+1 X^3+X+1 X^3+X^2+1 X^3+X+1 X^3+1 X^3+X^2  0
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  1 X^3+X^2+X X+1  X X^3+X^2+X  X X^3+X^2+X+1 X^3+X^2+1 X^3+X^2+1  1  1 X^2 X^2+X X^2+1 X^2 X^3+X^2 X^2+1  1 X^2+1 X^3+X^2+X+1 X^3+X  X X+1 X^2+X+1 X^3+X^2+1  0 X^3+X^2+X+1  0 X^3+X^2 X^3+X^2+X  1  1 X^3 X^3+X^2+X X+1 X^2  1  1 X^3+X+1 X^2+1  1 X^3+X^2 X^3+X^2+X+1 X^3+X+1 X^2 X+1 X^3+1 X^3+X+1 X^2+1 X^2+X+1  1 X+1 X^2+X X^3+1  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+104x^62+676x^63+627x^64+716x^65+422x^66+544x^67+279x^68+228x^69+150x^70+196x^71+48x^72+56x^73+28x^74+16x^75+2x^76+2x^80+1x^84

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 2.25 seconds.