The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+108x^62+576x^63+648x^64+752x^65+563x^66+456x^67+332x^68+232x^69+104x^70+128x^71+60x^72+88x^73+32x^74+8x^75+5x^76+1x^80+1x^82+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 0.234 seconds.