The generator matrix

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

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+68x^63+213x^64+628x^65+501x^66+496x^67+440x^68+506x^69+431x^70+440x^71+148x^72+144x^73+40x^74+18x^75+7x^76+2x^77+1x^78+4x^80+2x^82+2x^83+2x^88+1x^90+1x^92

The gray image is a code over GF(2) with n=544, k=12 and d=252.
This code was found by Heurico 1.16 in 0.421 seconds.