The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+101x^62+498x^63+956x^64+1326x^65+1178x^66+1160x^67+654x^68+740x^69+567x^70+414x^71+249x^72+122x^73+110x^74+72x^75+12x^76+20x^77+10x^78+2x^82

The gray image is a code over GF(2) with n=536, k=13 and d=248.
This code was found by Heurico 1.16 in 0.843 seconds.