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

generates a code of length 41 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+74x^38+120x^39+174x^40+324x^41+154x^42+82x^43+65x^44+16x^45+11x^46+2x^47+1x^74

The gray image is a code over GF(2) with n=328, k=10 and d=152.
This code was found by Heurico 1.16 in 0.047 seconds.