The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+98x^51+549x^52+1138x^53+1950x^54+2962x^55+4411x^56+6384x^57+7875x^58+9230x^59+11157x^60+12572x^61+13406x^62+12910x^63+11429x^64+10354x^65+8220x^66+6146x^67+4215x^68+2510x^69+1672x^70+902x^71+455x^72+244x^73+145x^74+70x^75+39x^76+12x^77+12x^78+2x^79+2x^81

The gray image is a code over GF(2) with n=248, k=17 and d=102.
This code was found by Heurico 1.13 in 207 seconds.