The generator matrix

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

generates a code of length 51 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+76x^43+923x^44+2678x^45+6517x^46+11812x^47+19769x^48+29934x^49+37158x^50+43118x^51+38100x^52+31058x^53+20310x^54+11314x^55+5632x^56+2318x^57+918x^58+266x^59+179x^60+24x^61+25x^62+2x^63+2x^64+4x^65+4x^67+2x^68

The gray image is a code over GF(2) with n=408, k=18 and d=172.
This code was found by Heurico 1.16 in 426 seconds.