The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2) 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 0.391 seconds.