The generator matrix

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

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+61x^56+228x^57+498x^58+478x^59+642x^60+408x^61+551x^62+476x^63+469x^64+160x^65+55x^66+34x^67+14x^68+4x^69+5x^70+4x^71+4x^72+2x^78+1x^82+1x^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 0.328 seconds.