The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+138x^51+504x^52+1078x^53+1416x^54+2556x^55+3072x^56+3920x^57+4733x^58+5648x^59+5801x^60+6846x^61+6573x^62+6102x^63+4850x^64+4208x^65+3051x^66+2106x^67+1279x^68+786x^69+323x^70+292x^71+109x^72+80x^73+30x^74+20x^75+10x^77+2x^79+2x^82

The gray image is a code over GF(2) with n=244, k=16 and d=102.
This code was found by Heurico 1.13 in 55.5 seconds.