The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+182x^35+1356x^36+2806x^37+5046x^38+8124x^39+9529x^40+11234x^41+10306x^42+7788x^43+4926x^44+2596x^45+1070x^46+396x^47+148x^48+18x^49+2x^50+6x^51+2x^53

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 20.7 seconds.