The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+143x^60+328x^61+404x^62+384x^63+458x^64+384x^65+306x^66+336x^67+247x^68+304x^69+218x^70+184x^71+129x^72+88x^73+84x^74+24x^75+42x^76+16x^77+6x^78+4x^80+6x^82

The gray image is a code over GF(2) with n=264, k=12 and d=120.
This code was found by Heurico 1.11 in 0.372 seconds.