The generator matrix

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

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+161x^36+96x^37+432x^38+280x^39+975x^40+304x^41+960x^42+224x^43+382x^44+112x^45+98x^46+8x^47+40x^48+12x^50+8x^52+2x^54+1x^60

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 0.25 seconds.