The generator matrix

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