The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+184x^57+66x^58+304x^59+253x^60+504x^61+260x^62+240x^63+47x^64+104x^65+10x^66+64x^67+2x^68+8x^69+1x^108

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 0.297 seconds.