The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  X  2  1  1  0  X  1  X  1  1  2  1  1  0  X  1  1  X  X  X  2  X  0
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  2  2 X+2  0  X X+2  0  X  2  X  X  X X+2 X+2  X  X  0  X  0 X+2  0 X+2  2  2  X  2  0  2 X+2  X  X  2  0  0  X X+2  0
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2  X  X  2  0 X+2 X+2  X  2  0  2  X  0  0 X+2 X+2 X+2  X  2  X  2  2  0  2  X X+2 X+2  X  X  X X+2  0  X X+2  X X+2  0  X
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  0  2  2  0  0
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  2  2  2  2  0  0  2  0  0  0  0  2  0  2  0  2  0  2  2  2  2  0  2  0  2  2  2  2  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  0  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  2  2  0  0  2  0  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+138x^44+8x^45+228x^46+64x^47+446x^48+184x^49+478x^50+272x^51+604x^52+248x^53+460x^54+160x^55+322x^56+72x^57+192x^58+16x^59+118x^60+48x^62+29x^64+2x^66+4x^68+2x^72

The gray image is a code over GF(2) with n=208, k=12 and d=88.
This code was found by Heurico 1.16 in 1.12 seconds.