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  X  1  X  1  1  1  1  1  2  1  1  2  1  1  X
 0 2X+2  0 2X+2  0 2X+2  0  2 2X 2X+2  0 2X+2 2X+2  0 2X  2  0 2X 2X+2  2 2X+2  2  0  0  0 2X 2X+2 2X+2 2X+2 2X+2 2X+2  2  2 2X+2 2X  0 2X 2X+2 2X+2  2 2X+2
 0  0 2X  0  0  0  0  0 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0 2X
 0  0  0 2X  0  0  0 2X  0  0  0 2X  0  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X  0 2X 2X
 0  0  0  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0  0  0 2X 2X  0  0 2X
 0  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X  0  0
 0  0  0  0  0  0 2X  0 2X  0 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0 2X 2X 2X  0 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+123x^36+16x^37+40x^38+128x^39+357x^40+736x^41+336x^42+128x^43+106x^44+16x^45+8x^46+41x^48+11x^52+1x^72

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 2.64 seconds.