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

generates a code of length 66 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+105x^60+84x^61+272x^62+324x^63+350x^64+744x^65+408x^66+744x^67+320x^68+324x^69+204x^70+84x^71+84x^72+18x^74+14x^76+8x^78+5x^80+2x^82+1x^108

The gray image is a code over GF(2) with n=528, k=12 and d=240.
This code was found by Heurico 1.16 in 0.672 seconds.