The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+295x^44+1350x^45+3216x^46+6416x^47+10113x^48+14924x^49+18206x^50+20982x^51+19370x^52+15636x^53+10166x^54+5796x^55+2632x^56+1286x^57+468x^58+142x^59+35x^60+18x^61+6x^62+8x^63+2x^64+2x^65+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 105 seconds.