The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) 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.