The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+502x^57+1031x^58+1716x^59+1903x^60+2368x^61+2107x^62+2112x^63+1608x^64+1344x^65+761x^66+460x^67+227x^68+136x^69+33x^70+56x^71+3x^72+2x^73+4x^74+8x^75+2x^76

The gray image is a code over GF(2) with n=496, k=14 and d=228.
This code was found by Heurico 1.16 in 367 seconds.