The generator matrix

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

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+654x^36+1000x^37+3236x^38+3384x^39+5717x^40+4976x^41+5572x^42+3632x^43+2982x^44+744x^45+652x^46+88x^47+113x^48+12x^50+4x^52+1x^56

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 261 seconds.