The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+141x^56+662x^57+1225x^58+1608x^59+2647x^60+3166x^61+4083x^62+4520x^63+5607x^64+5698x^65+6295x^66+6148x^67+5769x^68+4844x^69+4341x^70+2980x^71+2356x^72+1394x^73+938x^74+552x^75+294x^76+134x^77+70x^78+28x^79+15x^80+6x^81+6x^82+4x^83+2x^84+2x^86

The gray image is a code over GF(2) with n=264, k=16 and d=112.
This code was found by Heurico 1.13 in 61.4 seconds.