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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+138x^62+536x^63+767x^64+688x^65+468x^66+452x^67+314x^68+264x^69+179x^70+100x^71+76x^72+48x^73+37x^74+24x^75+1x^76+1x^78+1x^82+1x^84

The gray image is a code over GF(2) with n=528, k=12 and d=248.
This code was found by Heurico 1.16 in 0.25 seconds.