The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  X  1  2  1  1  1  X  1  1  1  X  1  X
 0  X  0  X 2X  0 3X  X 2X+2 3X+2 2X+2 3X+2  2 X+2 2X+2 3X+2  0 2X 3X 3X  0 2X+2 3X 3X+2 2X+2 X+2 2X 3X+2  2 3X+2  2  X  0 2X+2  X  X  2 3X 2X 3X 2X+2 3X  2  2 3X+2 X+2  0 X+2 2X  2 3X+2 2X+2 X+2 3X  2  X  0 2X+2 3X+2  X  0 2X+2  X 3X+2 X+2  2
 0  0  X  X 2X+2 3X+2 3X+2 2X+2 2X+2 X+2  X  2  0 3X 3X+2 2X  0 X+2 3X+2  2  2 3X+2 3X  2  2 X+2 3X 2X 2X 3X 3X  0 2X 3X 3X 2X 3X+2 2X+2  2 X+2  X 2X  2  2 X+2 3X+2 3X 2X  X  0  X X+2  2  0 X+2  0 2X+2  0 3X 2X+2 2X+2  0 3X+2  X  0 3X+2
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0 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+158x^62+108x^63+334x^64+224x^65+496x^66+228x^67+257x^68+56x^69+91x^70+12x^71+63x^72+8x^73+6x^74+4x^75+1x^78+1x^116

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 0.328 seconds.