The generator matrix

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

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+164x^37+330x^38+490x^39+598x^40+808x^41+675x^42+412x^43+223x^44+124x^45+76x^46+42x^47+37x^48+8x^49+6x^50+2x^52+2x^56+1x^66

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.