The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+68x^56+282x^57+430x^58+504x^59+414x^60+746x^61+449x^62+546x^63+318x^64+176x^65+72x^66+36x^67+28x^68+10x^69+5x^70+2x^71+3x^72+2x^73+3x^74+1x^90

The gray image is a code over GF(2) with n=488, k=12 and d=224.
This code was found by Heurico 1.16 in 0.39 seconds.