The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+98x^39+159x^40+128x^41+104x^42+106x^43+123x^44+90x^45+86x^46+60x^47+32x^48+20x^49+1x^50+4x^51+2x^52+2x^53+2x^55+2x^56+1x^58+2x^59+1x^60

The gray image is a code over GF(2) with n=172, k=10 and d=78.
This code was found by Heurico 1.16 in 3.45 seconds.