The generator matrix

 1  0  0  0  1  1  1 2X+2  1  1  1  1  0 X+2 3X+2  1 2X+2 2X+2  1 3X  1 3X+2  1  1 2X+2  1  1 X+2  1  0  1  1  1 2X  1  2 X+2  1  1  1 2X 3X+2  1  1  1  1 3X+2  1  1 3X  1  1
 0  1  0  0  0 2X+1  1  1 2X X+3 X+2 2X+3  1 3X+2  1 2X+2  0  1 X+1  1 X+1  1 3X+3 3X 3X+2  X  1  2 X+2  1  2 3X+3 2X+1  1  2 3X+2  1 3X+2 3X+2 X+1  2  0  1 2X 2X 3X  1  X X+3  1 X+1  2
 0  0  1  0  1  1  0  3 2X 2X+1 3X+1 3X 2X+1  1  X X+3 3X+2  0 X+3 X+3  X 3X+1 2X+2  X  1 3X+2 3X+3  1 2X+1 X+1 X+2 2X+2  0 3X 2X+1  1  1 2X+1 X+2 X+3 2X  1 X+3 X+1 2X+3 X+2  0 2X+3 3X+2 2X+1 X+2  2
 0  0  0  1  1  2  3  1 3X+1 3X+3 2X 3X 3X+2  3  3 X+2  1 3X X+1 3X+3  1 2X  2 2X  1  1 X+2 3X+2 X+1  0 2X 2X+1  0 2X+3 3X+1 3X  3 2X+2 3X+3 3X+2  1 X+3 2X+3  3 2X  3 X+1  2 3X+1 2X+3 3X+2 2X
 0  0  0  0 2X+2  0 2X+2 2X+2  2  2  0 2X 2X 2X+2 2X+2 2X  2  0 2X+2 2X+2  2 2X 2X+2 2X+2  0 2X  2  2 2X+2 2X+2  2  0  2  0 2X 2X+2  0  2 2X+2  2  2  2  0  2 2X+2  0 2X  0 2X  2  0  0

generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+132x^44+1066x^45+2731x^46+6436x^47+11594x^48+21234x^49+28533x^50+38874x^51+39348x^52+40260x^53+29942x^54+21270x^55+10953x^56+5832x^57+2333x^58+1048x^59+324x^60+130x^61+45x^62+34x^63+14x^64+6x^65+2x^67+2x^68

The gray image is a code over GF(2) with n=416, k=18 and d=176.
This code was found by Heurico 1.16 in 441 seconds.