The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  2  2  1  1  1  X  1 2X+2  1  1  1 2X+2  0  1  1  1  X  0 2X+2  X  1
 0  X  0  X  0 2X X+2  X  2 X+2  2 3X+2  2 2X+2 3X 3X+2 2X+2 2X+2 3X+2  X  X  2  2 X+2 3X+2 3X  X  X 3X 3X+2  0  X  0 3X 2X  2  X  X  X  X 2X+2
 0  0  X  X 2X+2 3X+2 X+2  2 2X+2 2X  0 2X+2  X X+2 X+2  X 3X 3X 2X+2  2 2X+2  X  2 X+2  2 X+2 3X+2 3X+2 3X+2 2X+2  2  0  X  X  X 3X+2 2X+2  0 X+2  X X+2
 0  0  0 2X  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0  0 2X  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0  0
 0  0  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0 2X  0 2X 2X 2X 2X  0  0  0 2X  0  0  0  0 2X  0 2X 2X  0 2X  0  0  0  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+53x^36+216x^37+386x^38+476x^39+705x^40+618x^41+646x^42+390x^43+262x^44+152x^45+84x^46+60x^47+28x^48+6x^49+3x^50+2x^51+7x^52+1x^58

The gray image is a code over GF(2) with n=328, k=12 and d=144.
This code was found by Heurico 1.16 in 0.203 seconds.