The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+398x^38+648x^39+994x^40+632x^41+544x^42+272x^43+257x^44+152x^45+154x^46+24x^47+19x^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 0.125 seconds.