The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+252x^39+229x^40+236x^41+109x^42+64x^43+41x^44+76x^45+2x^46+12x^47+1x^52+1x^58

The gray image is a code over GF(2) with n=328, k=10 and d=156.
This code was found by Heurico 1.16 in 49.5 seconds.