The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+526x^58+920x^59+1346x^60+1184x^61+1274x^62+680x^63+824x^64+440x^65+402x^66+288x^67+153x^68+72x^69+70x^70+11x^72+1x^76

The gray image is a code over GF(2) with n=496, k=13 and d=232.
This code was found by Heurico 1.16 in 16.9 seconds.