The generator matrix

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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+140x^63+520x^64+752x^65+772x^66+424x^67+448x^68+348x^69+233x^70+132x^71+101x^72+84x^73+89x^74+32x^75+8x^76+8x^77+1x^78+2x^80+1x^82

The gray image is a code over GF(2) with n=536, k=12 and d=252.
This code was found by Heurico 1.16 in 0.25 seconds.