The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+128x^55+434x^56+454x^57+716x^58+700x^59+837x^60+592x^61+815x^62+610x^63+773x^64+520x^65+514x^66+314x^67+345x^68+162x^69+117x^70+86x^71+42x^72+14x^73+12x^74+2x^75+2x^77+2x^78

The gray image is a code over GF(2) with n=248, k=13 and d=110.
This code was found by Heurico 1.13 in 1.15 seconds.