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

generates a code of length 66 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+188x^61+247x^62+392x^63+403x^64+724x^65+471x^66+634x^67+320x^68+278x^69+113x^70+116x^71+71x^72+64x^73+33x^74+26x^75+4x^76+10x^77+1x^104

The gray image is a code over GF(2) with n=528, k=12 and d=244.
This code was found by Heurico 1.16 in 11 seconds.