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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+11x^58+72x^59+52x^60+752x^61+52x^62+72x^63+11x^64+1x^122

The gray image is a code over GF(2) with n=488, k=10 and d=232.
This code was found by Heurico 1.16 in 0.203 seconds.