The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+138x^59+1230x^60+2264x^61+4155x^62+5456x^63+7388x^64+7820x^65+8855x^66+7696x^67+8014x^68+5220x^69+3678x^70+1900x^71+973x^72+402x^73+207x^74+54x^75+54x^76+16x^77+1x^78+4x^79+4x^80+6x^81

The gray image is a code over GF(2) with n=528, k=16 and d=236.
This code was found by Heurico 1.16 in 36.6 seconds.