The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+218x^36+388x^37+874x^38+1000x^39+1566x^40+1396x^41+1998x^42+1640x^43+2009x^44+1396x^45+1468x^46+952x^47+772x^48+332x^49+230x^50+56x^51+69x^52+8x^53+6x^54+5x^56

The gray image is a code over GF(2) with n=172, k=14 and d=72.
This code was found by Heurico 1.16 in 6.72 seconds.