The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+144x^63+620x^64+662x^65+684x^66+428x^67+504x^68+292x^69+305x^70+188x^71+85x^72+42x^73+97x^74+24x^75+6x^76+12x^77+1x^82+1x^86

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 0.265 seconds.