The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+130x^57+556x^58+678x^59+672x^60+540x^61+504x^62+262x^63+276x^64+182x^65+169x^66+72x^67+26x^68+24x^69+3x^70+1x^76

The gray image is a code over GF(2) with n=488, k=12 and d=228.
This code was found by Heurico 1.16 in 0.204 seconds.