The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+247x^58+460x^59+696x^60+472x^61+697x^62+468x^63+413x^64+180x^65+186x^66+100x^67+89x^68+44x^69+36x^70+4x^71+1x^74+1x^78+1x^84

The gray image is a code over GF(2) with n=496, k=12 and d=232.
This code was found by Heurico 1.16 in 0.391 seconds.