The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) 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 0.187 seconds.