The generator matrix

 1  0  0  1  1  1  X  1  1  2  1  1  X  2 X+2  0  1  1 X+2  1  X  1  1  1 X+2 X+2  1  X  1  2  1  0  1  1  1  0  1  1  1  0  X  1 X+2 X+2  0  1 X+2 X+2 X+2  1  1  1
 0  1  0  0  1  1  1  X X+3  1  X X+3  1  X  1  1 X+1 X+2  X  1  1 X+2 X+1  0  1  2  2  1 X+3  1 X+3  1  X  1 X+2  1  2  3 X+3  0  0  3  2  1  1  1  1  2  1  X  0 X+2
 0  0  1 X+1 X+3  0  1  X  3  3  1  X  X  1 X+1 X+2  0  2  1  1  X X+1 X+1 X+2  2  1  1  2  0  X  X X+1  X X+2  3 X+1 X+2 X+3  3  1  1 X+2  1 X+1 X+2  1 X+1  1 X+3 X+2 X+2  0
 0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  2  0  2  2  2  0  2  0  2  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  2
 0  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  2  2  2  2  0  0  2  0  2  0  0  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  2  2  2  2  0  0  0  2  0  2  2  2  0  2  2  2  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  2  2  0  0  2  0  0  2  0  2  2  2  2  2  0  2  0  2  0  0  0  0  0  0  2  2  0  0  0  0  0  0  2  0  0  2
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  0  0  0  2  0  2  2  0  0  0  2  2  0  2  2  2  2  0  0  2  0  0  0  2  2  0  2  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+238x^44+148x^45+732x^46+584x^47+1329x^48+960x^49+1802x^50+1400x^51+2066x^52+1240x^53+1888x^54+1208x^55+1334x^56+448x^57+508x^58+136x^59+238x^60+20x^61+52x^62+32x^64+10x^66+10x^68

The gray image is a code over GF(2) with n=208, k=14 and d=88.
This code was found by Heurico 1.16 in 9.52 seconds.