The generator matrix

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

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+103x^44+76x^45+398x^46+224x^47+674x^48+580x^49+987x^50+644x^51+1026x^52+680x^53+793x^54+552x^55+616x^56+260x^57+287x^58+52x^59+145x^60+4x^61+55x^62+25x^64+6x^66+2x^68+2x^70

The gray image is a code over GF(2) with n=208, k=13 and d=88.
This code was found by Heurico 1.16 in 3.23 seconds.