The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1 2X  1  1  X  1  1 3X+2  1 3X  1 X+2  1  1 2X+2  1  1  1  1  1  1 2X  X  1  1  2  1  1 3X+2  1  1  2  1  X  1  1  X  1 2X+2  2  1  X  1  1  X  1  1  1  X  1  1
 0  1 X+1 X+2 2X+3  1 2X 3X+3  1  2 X+1  1  X 2X+1  1 2X+2  3  1  1  1 3X+2  1 2X+3  2  1 3X X+3 3X+2  0 X+1 2X+1  1  1 3X 3X+3  1 3X+2  3  1 3X X+3  1 2X  0  0  1  1 2X+2  X  1 2X+3 3X 2X  3 X+2 X+1 3X 3X+1  2 3X X+1
 0  0 2X+2 2X+2 2X 2X+2  2  2 2X 2X  0  2  2  0  2 2X+2 2X+2 2X  2  0  0  2  0  0 2X+2 2X 2X 2X 2X 2X 2X 2X+2 2X+2  0  0  2  2  2  0 2X+2 2X+2  0 2X+2 2X  2 2X+2 2X  2  0 2X  2 2X 2X 2X 2X+2  2 2X+2 2X+2  2  0  0
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0 2X  0 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+464x^58+144x^59+440x^60+536x^62+96x^63+228x^64+118x^66+16x^67+2x^72+1x^80+2x^82

The gray image is a code over GF(2) with n=488, k=11 and d=232.
This code was found by Heurico 1.16 in 41 seconds.