The generator matrix

 1  0  0  1  1  1  2  1  1  1  1 X^2+X+2 X+2 X^2+X  1  1  1  0 X^2  X  1  X  1 X^2+X+2  1 X+2  1  1  1 X^2+2  1  1  1  X  1  1 X^2 X^2 X^2+2 X^2+2  1  X  2  1  1 X^2+X+2  1 X^2+X  1  1  1  1  1 X+2  1  1  1  2  0  1  1  0  1  1  1  1  1
 0  1  0 X^2 X^2+3 X^2+1  1 X+2  2 X+1 X^2+X+3  1  1  0 X^2 X^2+X X^2+1  1 X+2  1 X^2+X+1 X^2+X X^2+X+2  1  3  1 X+1 X^2+X+2 X^2+X+1  1 X+2 X^2+2 X+3 X^2+2  1 X+1  1  1  1  2 X+3  1  1  1  2  1  0  1  1 X+3 X^2+X+3  3 X+2  0  1  1 X^2+X X^2 X^2+X+2  0 X^2+X+2  X X^2+X X+2 X^2+1 X^2+1  0
 0  0  1 X^2+X+1 X^2+X+3 X^2+2 X+1 X^2+X+2 X^2+3  2 X^2+1 X^2+X+3  0  1  X X^2+1 X^2+X X^2+3  1 X^2+X+2 X+3  1 X^2+2 X^2+3  1 X^2 X^2+X X^2+X+1  2 X+2  3  0 X+3  1 X+2  3  3 X^2+2 X^2+X+3  1 X+1  1 X^2+X+2 X^2+X+3 X+1  1 X^2+3 X^2+X+2  3 X^2+3 X^2+X X+2 X^2+X  1  2 X+1 X^2+X+3  1  1 X^2+X+1 X^2+X+2  1  0 X^2+X+1  3 X^2+X+2  0
 0  0  0  2  2  2  0  2  0  0  0  2  2  2  0  2  0  2  2  2  0  0  0  0  0  0  0  2  2  0  0  2  0  0  2  2  0  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  0  0  2  0  2  0  0  2  0  2  2  0  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+105x^62+658x^63+821x^64+1298x^65+892x^66+1360x^67+712x^68+876x^69+504x^70+410x^71+203x^72+154x^73+61x^74+92x^75+22x^76+8x^77+5x^78+8x^79+1x^80+1x^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 0.766 seconds.