The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+646x^36+1112x^37+3212x^38+3304x^39+5849x^40+4936x^41+5518x^42+3496x^43+2833x^44+896x^45+760x^46+80x^47+102x^48+14x^50+9x^52

The gray image is a code over GF(2) with n=328, k=15 and d=144.
This code was found by Heurico 1.16 in 17.5 seconds.