The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+112x^52+578x^53+1136x^54+1688x^55+2087x^56+3154x^57+3835x^58+5016x^59+5533x^60+6300x^61+6304x^62+6638x^63+5510x^64+5208x^65+4102x^66+3156x^67+2009x^68+1432x^69+814x^70+434x^71+226x^72+154x^73+59x^74+24x^75+10x^76+6x^77+6x^78+4x^79

The gray image is a code over GF(2) with n=248, k=16 and d=104.
This code was found by Heurico 1.13 in 56.7 seconds.