The generator matrix

 1  0  0  1  1  1  2  1 3X+2  1 3X  1 3X+2  1 3X+2  1  1  2  1  1  1  0 X+2 X+2  1 3X+2  1  1  1  1  1 2X  X 2X  1  0  1  1  2 3X+2  1
 0  1  0  0  3 2X+3  1 3X 2X+2 3X+3  1 X+1  1 2X+2  1 X+2  3 X+2 2X+1 X+2 X+1  1  1  X  2  1 3X+1  3  1  2 2X+3  1 2X 3X+2 3X  1 2X 2X+2  0  1 2X
 0  0  1 X+1 X+1  0 3X+3 X+2  1 3X+1 2X  X X+1  3  X  2  1  1  X  3  1 3X+2 2X+3  1  0 3X+2 2X+2 2X+1 X+3  3 2X  X  1  1 3X+3  X X+2 X+2  1 2X+1 2X
 0  0  0 2X+2  2 2X 2X+2 2X  2  2  0 2X+2 2X 2X 2X+2 2X+2  0 2X  2  2 2X 2X 2X 2X+2 2X+2  2  0 2X+2 2X  0 2X+2  2  0  0  2  0 2X  0  2  0  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+133x^36+600x^37+1696x^38+1900x^39+2720x^40+2576x^41+2704x^42+1722x^43+1411x^44+522x^45+253x^46+88x^47+37x^48+12x^49+2x^50+2x^51+2x^52+2x^53+1x^54

The gray image is a code over GF(2) with n=328, k=14 and d=144.
This code was found by Heurico 1.16 in 1.59 seconds.