The generator matrix

 1  0  1  1  1 X+2  1  1 3X  1  1 3X+2 X+2 2X+2  1  1  1  1 3X  1 2X+2  1 X+2  1  1  1  1  X 2X+2 2X  2 2X+2  X  1  1  1  1  0  X  0  1
 0  1  1 2X+2 X+1  1  X 2X+1  1 3X 3X+3  1  1  1 2X+2  3 3X X+1  1 2X  1 X+3  1  X 2X+1  0 3X+3  1  X  1  1  1  1 3X+2  1  3 X+2  1  0  0  X
 0  0  X 3X 2X 3X 3X 2X X+2  0  X  0  2 2X+2 X+2  2 X+2 2X+2  X  2 3X 3X+2 X+2  2 3X+2 3X+2  2  0 3X+2 X+2 2X  X  2  0  2  X X+2 3X 3X  X 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+176x^38+388x^39+395x^40+360x^41+278x^42+176x^43+123x^44+88x^45+29x^46+12x^47+16x^48+4x^50+1x^52+1x^54

The gray image is a code over GF(2) with n=328, k=11 and d=152.
This code was found by Heurico 1.16 in 0.062 seconds.