The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  2  1  1  1  1  1  1  X  X  1  2  1  1  X  0 X^2+2  1  X  1  X  X  0
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  0 X^2+X  2 X^2+X X+2 X^2 X^2  X  0 X^2+X X^2 X+2  2  2 X+2 X+2 X+2 X^2  0 X+2  0 X^2+X X^2+X  0 X^2+X X^2+X+2 X^2 X+2 X^2+2 X^2+X+2 X^2  X  2 X^2+X  0 X^2+X+2 X+2 X^2+2 X^2 X+2 X^2+X  X  X X^2+X  X  X  X X^2+2 X+2  0 X^2+X+2  X  X
 0  0 X^2+2  0 X^2  0  2  0 X^2 X^2  2 X^2+2 X^2+2 X^2+2  0 X^2  0 X^2+2  2 X^2+2 X^2 X^2  2  2  0  2  0 X^2 X^2 X^2 X^2 X^2  0 X^2+2  0  2 X^2  2  0 X^2 X^2  0 X^2+2  0 X^2+2 X^2+2 X^2+2 X^2+2 X^2  2  2  2  2  2  0 X^2+2 X^2+2  2 X^2  0  2
 0  0  0 X^2+2  0  2  2 X^2 X^2 X^2 X^2  0  0 X^2 X^2+2 X^2  2 X^2+2 X^2+2  2  0 X^2+2  2 X^2+2 X^2+2 X^2  0  2  0 X^2+2 X^2 X^2+2  0 X^2  2  0 X^2+2 X^2+2 X^2+2  2  2 X^2  0  0  2  2  0 X^2+2  2 X^2+2  0  2 X^2  0  0 X^2 X^2 X^2  2  2  2
 0  0  0  0  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  0  0  2  2  0  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  0  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  2  2  0

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+343x^56+40x^57+408x^58+224x^59+862x^60+496x^61+704x^62+224x^63+502x^64+40x^65+136x^66+86x^68+25x^72+4x^76+1x^96

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 130 seconds.