The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+191x^44+1330x^45+3477x^46+6130x^47+10744x^48+13804x^49+19705x^50+19810x^51+20057x^52+14668x^53+10766x^54+5722x^55+2840x^56+1100x^57+507x^58+142x^59+54x^60+10x^61+7x^62+4x^63+1x^64+2x^66

The gray image is a code over GF(2) with n=408, k=17 and d=176.
This code was found by Heurico 1.16 in 110 seconds.