The generator matrix

 1  0  0  1  1  1  2  2 2X+2  1  1  2  1  1 3X  1  1 X+2 3X+2  1  1  1  X  1  1 2X+2 3X+2  1  1 2X  1  1  1  1 2X  1  1  1  1  1 X+2  1 3X  X  1  0  1 X+2  X 3X+2  0  1  2 3X+2 2X  1  1  X  2 3X  1  1
 0  1  0  0 2X+3 2X+3  1 3X  1 2X  3  1  2 2X+1 3X+2  X 3X+1  1  1 3X X+1 3X+2  1 X+2 X+1  1  0  X 3X+3  1 X+3 2X 2X+2  1  X  1 2X+2  3 2X+2 X+3 3X+2  1  1  0 3X+2 2X 2X+3 2X+2  1  1  1  1 X+2  1  1  2 X+3  1 2X+2  X X+1 2X+2
 0  0  1 X+1 3X+1 2X X+3  1  X 3X  X  3 2X+3  3  1 2X+1 3X X+3 X+2  2  3 X+2  0 2X+1 2X 3X+1  1 X+1 3X+1  1 2X 2X+2 2X+1 2X+3  1  0 3X+3 2X+2  2 X+3  1 X+1  1  1  0  1 3X+2  1 3X+3 2X+2  X 3X  1  1  0 X+1 2X+1 3X  1  1  X X+2
 0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X  0  0  0 2X 2X  0 2X  0  0  0  0 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0  0  0 2X  0 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+730x^58+688x^59+1312x^60+856x^61+1714x^62+728x^63+873x^64+296x^65+410x^66+216x^67+262x^68+32x^69+54x^70+14x^72+4x^74+2x^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 120 seconds.