The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X+2  1  1  1  1 X^2  2  1  1  1  1  1  2  1 X+2  1  X  1  X  1 X^2 X^2+X  1  1  1  X X+2  1  1 X^2 X^2+X  1  1 X^2+X+2 X^2 X^2+2  1  1  1  1  1 X^2+2 X^2+X+2  1  1 X^2+X X+2  X  2  1  1  1  2  0  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+1 X^2+X+2  1  1  0 X^2+3  2  3  1  1 X^2+X X+1  X X+1 X^2+2  1  1  1 X^2  1 X^2+X+3  1 X^2+X  1  1 X^2+1  1 X+2  0  1 X+1  2  X  1 X^2+3 X^2+X  1  1  1 X^2+3 X^2 X^2+X X^2+2 X+3  1  1 X^2 X^2+X+3  1  1 X^2+X+2  X X^2+1  0  2  1  2  1
 0  0  X  0 X+2  X X+2  2  0  2 X+2 X^2+X+2 X^2 X^2+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X+2 X^2+X X^2 X^2 X^2+X X^2+X X^2+2 X^2 X^2+X+2 X^2 X^2+2 X^2+X+2  0  0 X^2+2  X  2 X^2+X+2 X^2+X X+2  X X^2  X X+2 X^2+X X^2+X X^2  0 X^2+X  2  X X+2  X  2  0  0 X+2 X^2+2 X+2 X^2+2  2 X^2+X+2 X^2+X+2 X^2  2  0  0  X X+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  2  0  0  0  0  2  2  2  0  2  2  2  0  2  0  0  0  2  2  0  0  2  0  2  2  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+294x^63+538x^64+602x^65+597x^66+496x^67+445x^68+304x^69+299x^70+218x^71+143x^72+94x^73+13x^74+32x^75+8x^76+8x^77+2x^78+1x^84+1x^86

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 0.531 seconds.