The generator matrix

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

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+118x^56+288x^57+296x^58+576x^59+402x^60+800x^61+332x^62+672x^63+242x^64+192x^65+104x^66+32x^67+30x^68+4x^70+4x^72+1x^80+2x^88

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 0.312 seconds.