The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+176x^61+271x^62+324x^63+563x^64+564x^65+623x^66+426x^67+456x^68+226x^69+161x^70+104x^71+63x^72+64x^73+33x^74+26x^75+4x^76+10x^77+1x^104

The gray image is a linear code over GF(2) with n=528, k=12 and d=244.
This code was found by Heurico 1.16 in 3.39 seconds.