The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+636x^55+1982x^56+4280x^57+7571x^58+10420x^59+14655x^60+16520x^61+18829x^62+16682x^63+15228x^64+10602x^65+7011x^66+3700x^67+1727x^68+774x^69+298x^70+112x^71+17x^72+14x^73+2x^74+6x^76+2x^77+2x^79+1x^86

The gray image is a code over GF(2) with n=496, k=17 and d=220.
This code was found by Heurico 1.16 in 174 seconds.