The generator matrix

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

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+454x^57+1071x^58+1712x^59+2174x^60+1864x^61+2368x^62+2154x^63+1551x^64+1322x^65+812x^66+426x^67+222x^68+96x^69+108x^70+26x^71+9x^72+8x^73+1x^74+2x^75+2x^76+1x^80

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 44.5 seconds.