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  1  X  X  X  0  1  X  1  X  1  X  X  0  0  1  1  1  2  X  1  0  2  2  1  1  X
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2  0 X+2 X+2  0 X+2  2  0  0  2 X+2 X+2  2 X+2  X  X X+2  2  2 X+2 X+2  2  X  0  X X+2  X  0  X  0  X  X  2  X X+2  X
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  0  2  0  0  2  X  X  2  X  X X+2  X  0  2  X  2  X  0  2  X  X X+2  2  0  X X+2  2  2  0 X+2 X+2  2  X  0  X
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0  2 X+2  0 X+2 X+2  X  X  0  0  0 X+2  0  0  0  X  0  2  X  2  X  2  0  X  0  X  X  X  X  2  2  X  X X+2 X+2  0
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0  2  0  2  2  2  2  2  0  2  0  2  2  0  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  2  2  2  0  2  2  0  2  0  2  2  2  2  0  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  2  0  0  2  0  2  2  0  0  2  0  0  2  2  0  0  2  2  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+99x^44+16x^45+272x^46+128x^47+308x^48+392x^49+271x^50+456x^51+256x^52+608x^53+240x^54+272x^55+229x^56+136x^57+190x^58+40x^59+107x^60+40x^62+21x^64+11x^66+2x^68+1x^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 0.964 seconds.