The generator matrix

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

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+120x^62+540x^63+790x^64+584x^65+624x^66+464x^67+237x^68+196x^69+236x^70+128x^71+72x^72+68x^73+28x^74+4x^75+2x^76+1x^80+1x^84

The gray image is a code over GF(2) with n=528, k=12 and d=248.
This code was found by Heurico 1.16 in 0.266 seconds.