The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+60x^31+340x^32+974x^33+1837x^34+3190x^35+5196x^36+7250x^37+10050x^38+13046x^39+15220x^40+16272x^41+15042x^42+13454x^43+10940x^44+7338x^45+4954x^46+2894x^47+1533x^48+832x^49+367x^50+188x^51+48x^52+36x^53+4x^54+2x^56+2x^57+2x^58

The gray image is a code over GF(2) with n=164, k=17 and d=62.
This code was found by Heurico 1.13 in 117 seconds.