The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+90x^38+130x^39+316x^40+224x^41+318x^42+148x^43+221x^44+124x^45+157x^46+82x^47+97x^48+48x^49+72x^50+8x^51+5x^52+4x^53+3x^54

The gray image is a code over GF(2) with n=172, k=11 and d=76.
This code was found by Heurico 1.16 in 0.127 seconds.