The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1 X+2  1  2  X  X  2  1  0  1  2  1  1  1  X  1  1  1  1  0  2  X  1  1  1  1  0  1  X  1  1  1
 0  1  0  0  0  1  2  3  1 X+2  0 X+1  1  1  1  1  1  2  0  0 X+2 X+2  3 X+3 X+3  X X+1 X+2  X  X  2  1  1  0  0  3  3  1  X  2 X+1  X  1
 0  0  1  0  0  1  3  2  3  1  1  3  X X+2  1  X  2  1 X+3  1  1  0 X+3  X X+2  1  X X+3  X  3  1  0 X+3 X+1  2 X+1 X+1  1 X+3  1  1  0 X+1
 0  0  0  1  1  2  1  3  3  0 X+3  3 X+3 X+2  X  1  0  X  3  1 X+2  1 X+3 X+2  0 X+3  3 X+3  3  X X+3 X+2 X+1 X+3 X+1  X  2 X+2  1  2  2 X+2  1
 0  0  0  0  X  0  0  0  0 X+2  X  X  X X+2 X+2  X  2  2  2 X+2  X  2  X  2  2  2 X+2 X+2  0  2  0  X  0  0  2 X+2  2  2  X X+2  X  X  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+154x^36+482x^37+820x^38+1092x^39+1461x^40+1674x^41+1632x^42+1782x^43+1783x^44+1652x^45+1408x^46+1034x^47+694x^48+356x^49+200x^50+90x^51+35x^52+26x^53+4x^54+2x^55+2x^57

The gray image is a code over GF(2) with n=172, k=14 and d=72.
This code was found by Heurico 1.13 in 2.62 seconds.