The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^59+1196x^60+2558x^61+3942x^62+5788x^63+7207x^64+7648x^65+8790x^66+7764x^67+7645x^68+5324x^69+3529x^70+2144x^71+964x^72+466x^73+208x^74+112x^75+41x^76+18x^77+11x^78+4x^79+2x^80+2x^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 36.1 seconds.