The generator matrix

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

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+132x^63+232x^64+252x^65+242x^66+340x^67+291x^68+220x^69+154x^70+136x^71+35x^72+8x^73+2x^74+1x^78+1x^92+1x^94

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 0.235 seconds.