The generator matrix

 1  0  0  1  1  1  2  1  1 X^2+X  1 X^2+X  1 X^2+X+2  1  1 X^2 X+2 X^2+X  1  1  1 X^2+X  1 X^2+2  2  1  1  X  1  X  1 X^2+X+2  1 X^2+2  1  1  1  1 X^2+X X^2 X^2+2  1  1  2  0  1 X^2+2  1 X^2+X  1 X^2+2  1 X^2  1 X^2+2  1 X^2+X  X X+2  1
 0  1  0 X^2 X^2+3 X^2+1  1  0 X^2+2  2 X^2+X+1  1 X+3  1 X+2  3  1  1 X+2 X+1  X X^2+X  1  1  1  X X^2+X+1  X X^2+X  2  1 X^2+3  1 X^2 X+2 X^2+2 X^2+1 X^2+X+1 X+1  1  0  1 X+3 X^2+X  1  1  2 X+2 X^2+X X^2+2 X^2+1  0 X^2+1  1  X  1  1  1  X  1  0
 0  0  1 X^2+X+1 X^2+X+3 X^2+2 X^2+X+1 X^2+X  3  1 X^2  2 X^2+3 X^2+X+1 X^2+X+2 X^2+X+2  X  3  1 X^2+X+3  1  0 X^2+X X^2+3 X^2+1  1 X^2+X X^2+X+1  1  3 X+2 X^2  3 X+1  1 X^2+X X^2+1  1 X^2  0  1 X^2 X+3  3 X^2 X+2 X^2+1  1 X^2+X+1  1 X+2  1 X^2+3  1 X^2+X+1  2 X^2+X+1 X^2+X+3  1 X+2  0
 0  0  0  2  2  2  0  2  0  2  0  2  0  2  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  2  0  0  2  0  2  0  0  0  0  0  2  0  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+86x^56+566x^57+867x^58+1220x^59+1118x^60+1148x^61+863x^62+984x^63+425x^64+350x^65+237x^66+180x^67+86x^68+32x^69+22x^70+4x^72+2x^74+1x^78

The gray image is a code over GF(2) with n=488, k=13 and d=224.
This code was found by Heurico 1.16 in 0.656 seconds.