The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  1  1  X  1  1  X  1
 0 2X  0  0  0  0  0 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0  0
 0  0 2X  0  0  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0
 0  0  0 2X  0  0  0 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0
 0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X  0  0 2X 2X 2X  0  0  0 2X  0 2X  0  0  0 2X 2X  0 2X
 0  0  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X  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+38x^36+16x^38+223x^40+512x^41+176x^42+38x^44+11x^48+4x^52+4x^56+1x^72

The gray image is a code over GF(2) with n=328, k=10 and d=144.
This code was found by Heurico 1.16 in 0.328 seconds.