The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+294x^55+1064x^56+2106x^57+2775x^58+3820x^59+4269x^60+4662x^61+4290x^62+3636x^63+2473x^64+1656x^65+871x^66+452x^67+210x^68+102x^69+40x^70+38x^71+6x^72+2x^73+1x^76

The gray image is a code over GF(2) with n=488, k=15 and d=220.
This code was found by Heurico 1.16 in 8.94 seconds.