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

generates a code of length 67 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+124x^63+622x^64+612x^65+700x^66+672x^67+343x^68+300x^69+260x^70+112x^71+158x^72+64x^73+64x^74+36x^75+24x^76+3x^80+1x^84

The gray image is a code over GF(2) with n=536, k=12 and d=252.
This code was found by Heurico 1.16 in 0.25 seconds.