The generator matrix

 1  0  1  1  1 X^2+X  1  1  2  1  1 X^2+X+2  1 X^2+2  1  1 X+2  1 X^2  X  1  1  1  1  0 X^2+X  1  1  1  1  1  1 X^2+2 X+2  1  1  1  1  2  1  1 X^2+X+2  1  1  1 X^2  X  1  X  1  1  1  1  1  0 X^2+X+2  0  X  0 X^2  1  1  1  1  2 X^2  1
 0  1 X+1 X^2+X X^2+1  1  3  2  1 X^2+X+1 X^2+X+2  1 X^2  1 X^2+3  X  1 X+1  1  1 X^2+X+3 X^2+2 X+2  1  1  1 X+3  1  0 X+2 X^2+X+1 X^2+3  1  1 X^2+2 X^2+X  0 X+1  1 X^2+X X^2+1  1 X^2+2 X+2  3  1  1 X^2+X+3 X^2+X X^2+1  3 X+3 X+3 X+3  1  1  X  1  1  0  2  2 X^2  2  X  0 X^2+2
 0  0 X^2  0  2  0  2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2  0 X^2+2 X^2+2  0  0 X^2 X^2+2  0  2  2 X^2  2  2 X^2+2 X^2+2  0  2 X^2 X^2  2  2  2  0 X^2  0 X^2 X^2+2  2 X^2+2 X^2 X^2+2  2 X^2 X^2+2  0  2 X^2+2 X^2  2 X^2  2 X^2+2  2  0  0 X^2+2  2 X^2+2  2 X^2+2  2 X^2 X^2+2  0
 0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  0  2  2  0  2  0  2  0  2  0  0  2  2  2  0  0  2  0  2  0  2  0  2  2  0  0  2  2  0  0  2  2  2  0  0  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 63.

Homogenous weight enumerator: w(x)=1x^0+98x^63+304x^64+328x^65+202x^66+312x^67+233x^68+164x^69+172x^70+134x^71+43x^72+52x^73+2x^82+1x^84+2x^88

The gray image is a code over GF(2) with n=536, k=11 and d=252.
This code was found by Heurico 1.16 in 0.328 seconds.