The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+14x^56+104x^57+314x^58+392x^59+334x^60+592x^61+594x^62+608x^63+379x^64+376x^65+232x^66+88x^67+38x^68+16x^69+10x^70+2x^74+2x^88

The gray image is a code over GF(2) with n=496, k=12 and d=224.
This code was found by Heurico 1.16 in 0.328 seconds.