The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+125x^36+794x^37+1232x^38+2406x^39+2208x^40+3068x^41+2207x^42+2316x^43+1041x^44+624x^45+190x^46+122x^47+17x^48+8x^49+19x^50+4x^51+2x^53

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 1.67 seconds.