The generator matrix

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

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+468x^38+652x^39+831x^40+644x^41+536x^42+356x^43+327x^44+124x^45+116x^46+16x^47+24x^48+1x^52

The gray image is a code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 0.109 seconds.