The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1  1 3X  1  1  0  1  1 3X+2  1  1  2  1 3X  1  1  1  1  1  1  1  1  1  0 3X+2 2X X+2  1  1  1  1  1  1  1  1  1  1  1  1 2X 2X+2 3X+2  1  1  1
 0  1 X+1 3X+2 2X+3  1 X+3  2  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X 2X+1  1  0 X+1  1 3X+2 2X+3  1  2 X+3  1 3X  1 2X+1  3 X+1  1 X+3  0 3X+2  2 X+2  1  1  1  1 2X+3 3X+1 3X+3 2X+1 2X+3 X+1 2X+1 X+3 2X 2X+2 3X  X  X  1  1  3 2X+3  0
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X
 0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 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+139x^62+180x^63+356x^64+184x^65+334x^66+256x^67+270x^68+136x^69+165x^70+12x^71+12x^72+1x^78+1x^88+1x^94

The gray image is a code over GF(2) with n=528, k=11 and d=248.
This code was found by Heurico 1.16 in 0.219 seconds.