The generator matrix

 1  0  1  1 2X+2  1  1  1 3X+2  1  1  2  1  0  1  1  1  1  2  1  2  1  1  0 2X 3X  X X+2  1  1  1 3X+2  1 3X  1 2X  1  1  1  1  1 X+2  1  1  1  1  X  1  1  1  X  1  2  1  0  1 3X  1 2X  2  1 3X  1  X  0  1  0
 0  1  1 3X+2  1 3X+3 2X+2 2X+3  1 X+1  X  1 2X+2  1 X+1 2X  X  1  1 X+3  1 X+2  3  1  1  1  1  1  0 X+3 2X+3  1 3X  1 2X+2 2X  3 3X 2X 3X+1  3  1 3X 3X+3 X+3 2X+3  1 2X+2  1 2X+1  2 X+1  1 3X+2  1  2  1 3X+2  1  1 3X  1  2  0  1  1  1
 0  0  X  0 3X  X 3X 2X  0 2X 3X X+2 X+2  2  2 2X+2 X+2 3X+2 X+2 3X+2  X 2X+2  2  0 2X+2 2X  X  X 3X+2  0 X+2 X+2  2 2X+2  2  X  0  X 3X 3X+2 2X+2 X+2 X+2  X 2X+2 3X  2 2X  2 3X 3X  2 2X  0  X  0 3X+2 3X+2 2X  0  0 2X 3X+2 3X+2 X+2 X+2 3X+2
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X  0  0  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X 2X  0  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+290x^63+520x^64+590x^65+520x^66+606x^67+468x^68+372x^69+232x^70+214x^71+164x^72+66x^73+22x^75+12x^76+12x^77+4x^79+1x^80+2x^88

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 0.5 seconds.