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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+84x^63+651x^64+892x^65+1299x^66+1004x^67+1198x^68+684x^69+916x^70+404x^71+383x^72+288x^73+207x^74+76x^75+77x^76+20x^77+2x^78+1x^80+4x^81+1x^84

The gray image is a code over GF(2) with n=544, k=13 and d=252.
This code was found by Heurico 1.16 in 0.797 seconds.