The generator matrix

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

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+97x^36+24x^37+132x^38+184x^39+459x^40+344x^41+398x^42+200x^43+95x^44+16x^45+40x^46+35x^48+6x^50+16x^52+1x^64

The gray image is a code over GF(2) with n=328, k=11 and d=144.
This code was found by Heurico 1.16 in 0.11 seconds.