The generator matrix

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

generates a code of length 52 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+318x^44+746x^45+1108x^46+1650x^47+2038x^48+2520x^49+2962x^50+3210x^51+3544x^52+3400x^53+2986x^54+2640x^55+2074x^56+1518x^57+1014x^58+530x^59+232x^60+130x^61+90x^62+34x^63+15x^64+6x^65+2x^68

The gray image is a code over GF(2) with n=208, k=15 and d=88.
This code was found by Heurico 1.13 in 14 seconds.