The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+82x^57+296x^58+432x^59+388x^60+562x^61+682x^62+512x^63+417x^64+352x^65+228x^66+72x^67+24x^68+20x^69+10x^70+6x^73+8x^75+2x^77+2x^88

The gray image is a code over GF(2) with n=496, k=12 and d=228.
This code was found by Heurico 1.16 in 0.39 seconds.