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

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+301x^60+84x^62+494x^64+360x^66+474x^68+68x^70+190x^72+65x^76+10x^80+1x^112

The gray image is a code over GF(2) with n=264, k=11 and d=120.
This code was found by Heurico 1.16 in 45.6 seconds.