The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+311x^56+1224x^57+1992x^58+2620x^59+3993x^60+4232x^61+4782x^62+3892x^63+3672x^64+2624x^65+1732x^66+876x^67+396x^68+224x^69+122x^70+36x^71+14x^72+16x^73+4x^74+5x^76

The gray image is a code over GF(2) with n=496, k=15 and d=224.
This code was found by Heurico 1.16 in 9.5 seconds.