The generator matrix

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

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+40x^36+60x^37+92x^38+158x^39+200x^40+190x^41+213x^42+230x^43+196x^44+214x^45+136x^46+96x^47+55x^48+42x^49+67x^50+24x^51+16x^52+6x^53+3x^54+2x^55+4x^56+2x^59+1x^62

The gray image is a code over GF(2) with n=172, k=11 and d=72.
This code was found by Heurico 1.16 in 0.21 seconds.