The generator matrix

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

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+112x^58+518x^59+756x^60+684x^61+547x^62+426x^63+329x^64+300x^65+166x^66+92x^67+80x^68+44x^69+20x^70+16x^71+1x^72+3x^74+1x^76

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 0.235 seconds.