The generator matrix

 1  0  0  0  1  1  1  2  1  1  1 X+2  1  1  0  X  1  1  1  2  0  X  X  0 X+2  2  1  1 X+2  1  1  2  1  X  1  1  1  1  2  2  1  1  1  1  0  0 X+2  1  1  1  2  1
 0  1  0  0  0  1  3  1  2  2  2  0  1  3  1  1 X+2  X  1 X+2  1  1 X+2  1  1  X X+1  3  1 X+3  2  1  0  1 X+2  0  3  3  1 X+2 X+2  2 X+2 X+2  2 X+2  1  3  0 X+1  1  0
 0  0  1  0  1  1  2  3  3  0 X+1  1  1 X+2  X  1 X+1  X X+1  1  X X+1  1  1  X  0  0 X+3  2  0  2 X+1  2 X+3  3 X+1  3  X  0  0 X+2  3 X+3  X  1  X X+1  3 X+2  2  2  0
 0  0  0  1  1  2  1  1  3  1  X  1  3 X+2  1  2  2 X+1  X X+1  1 X+2  0 X+1  3  1  X  3  X  3 X+3 X+1 X+2  0 X+1  0 X+2  1  3  1  0 X+3  0 X+2  3  1  3 X+1  X  1  3  0
 0  0  0  0  X  0  0  0  0  2  0 X+2 X+2  X X+2  X  X X+2 X+2  0  2  2  2  X  0 X+2  2  X X+2  X  0 X+2 X+2 X+2 X+2  2  2  2  X  2 X+2  2  0 X+2 X+2  2  X  0  2 X+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+117x^44+398x^45+573x^46+874x^47+1029x^48+1394x^49+1368x^50+1740x^51+1476x^52+1734x^53+1461x^54+1324x^55+1041x^56+824x^57+426x^58+276x^59+139x^60+112x^61+40x^62+26x^63+3x^64+2x^65+4x^66+2x^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 8.63 seconds.