The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+77x^62+304x^63+472x^64+388x^65+513x^66+672x^67+503x^68+432x^69+341x^70+228x^71+105x^72+12x^73+27x^74+4x^75+2x^76+1x^78+4x^79+2x^80+4x^83+2x^84+1x^92+1x^94

The gray image is a code over GF(2) with n=536, k=12 and d=248.
This code was found by Heurico 1.16 in 0.484 seconds.