The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  1  1  X  X 2X+2  1
 0  X  2 3X+2  0 3X+2  2 3X  2 3X+2  0 3X 2X 3X  2 3X+2 2X+2 X+2  0 3X  0 2X 3X+2 X+2  2  2 3X 3X  0 X+2  0 2X  2 3X+2 3X+2 2X+2  X 3X+2 3X+2  2 3X
 0  0 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0 2X 2X  0
 0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0  0 2X 2X 2X  0  0  0  0 2X  0  0 2X  0  0  0  0  0 2X 2X
 0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0 2X  0  0  0  0  0  0 2X  0 2X
 0  0  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0  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+28x^36+172x^37+52x^38+216x^39+50x^40+988x^41+47x^42+288x^43+44x^44+116x^45+28x^46+8x^47+5x^48+4x^49+1x^74

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.