The generator matrix

 1  0  1  1  1 X+2  1  1  2  X  1  1  1  1  X  1  2  1  1 X+2  0  1  1  1  1  1  X  X  1  1 X+2  1  1  1  X  1  1  X  1  1  1 X+2  1  1  2  1  X  1  0  1  0  1
 0  1  1  0 X+3  1  X X+1  1  1 X+2  3 X+1 X+2  1  2  1  1 X+1  1  1  X  1  0 X+3  0  1  1 X+1  2  1  1  3 X+3  1 X+2  0  1 X+2  3  X  1 X+2  0  1 X+3  1  3  1 X+1  X  2
 0  0  X  0 X+2  0  0  0  2  2  0  2  X  X X+2 X+2  X  0  2 X+2  X  0  X  2  X X+2  2  0  0  X  X  X  X  2  2 X+2 X+2 X+2 X+2 X+2  2  0  2  0 X+2  X X+2  0  0  0 X+2  X
 0  0  0  X  0  0  X  2 X+2  X  0  0  X  X  0  2  X  X X+2  X  0  X  2  2 X+2  X  X  0  2  2  X  X  X  X  0  0 X+2  2  X X+2 X+2  0 X+2  X  X  0 X+2  X  2 X+2  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  0  0  2  2  0
 0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  0  2  2  2  0  2  0  2  2  2  2  0  0  2  0  0  0  0  2  0  2  0  2  2  2  0  2  2  0  2  2  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  2  2  2  2  0  0  2  0  0  2  0  0  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+128x^44+40x^45+331x^46+276x^47+736x^48+528x^49+899x^50+652x^51+1007x^52+808x^53+964x^54+428x^55+560x^56+288x^57+298x^58+52x^59+102x^60+63x^62+23x^64+3x^66+3x^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 3.2 seconds.