The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+48x^59+162x^60+608x^61+152x^62+48x^63+4x^64+1x^120

The gray image is a code over GF(2) with n=488, k=10 and d=236.
This code was found by Heurico 1.16 in 20 seconds.