The generator matrix

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

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+152x^57+200x^58+268x^59+269x^60+304x^61+224x^62+296x^63+174x^64+120x^65+24x^66+12x^67+1x^68+1x^76+1x^80+1x^84

The gray image is a code over GF(2) with n=488, k=11 and d=228.
This code was found by Heurico 1.16 in 0.203 seconds.