The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+148x^43+991x^44+2616x^45+6351x^46+11896x^47+19614x^48+29246x^49+38924x^50+41416x^51+39744x^52+30088x^53+20393x^54+11404x^55+5471x^56+2368x^57+964x^58+302x^59+123x^60+48x^61+22x^62+8x^64+2x^65+2x^66+2x^67

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 395 seconds.