The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+130x^35+478x^36+1046x^37+1458x^38+1874x^39+2442x^40+3186x^41+3774x^42+3784x^43+3850x^44+3354x^45+2606x^46+2044x^47+1275x^48+766x^49+402x^50+158x^51+80x^52+32x^53+16x^54+10x^55+2x^56

The gray image is a code over GF(2) with n=172, k=15 and d=70.
This code was found by Heurico 1.13 in 9.39 seconds.