The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) 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.