The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+594x^62+992x^63+1306x^64+1152x^65+1016x^66+872x^67+756x^68+520x^69+354x^70+232x^71+256x^72+56x^73+52x^74+16x^75+16x^76+1x^80

The gray image is a code over GF(2) with n=528, k=13 and d=248.
This code was found by Heurico 1.16 in 6.19 seconds.