The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+50x^54+252x^55+770x^56+1410x^57+2180x^58+3438x^59+4571x^60+5902x^61+7595x^62+9248x^63+11219x^64+12302x^65+12479x^66+12482x^67+11305x^68+9792x^69+8121x^70+6176x^71+4633x^72+2980x^73+1787x^74+1052x^75+596x^76+340x^77+166x^78+106x^79+53x^80+36x^81+6x^82+12x^83+4x^84+6x^85+2x^87

The gray image is a code over GF(2) with n=264, k=17 and d=108.
This code was found by Heurico 1.13 in 227 seconds.