The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+124x^35+1206x^36+2656x^37+5314x^38+7400x^39+10328x^40+11276x^41+10690x^42+7848x^43+4944x^44+2112x^45+1198x^46+304x^47+93x^48+20x^49+14x^50+4x^51+2x^52+2x^56

The gray image is a code over GF(2) with n=328, k=16 and d=140.
This code was found by Heurico 1.16 in 19.6 seconds.