The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+310x^37+732x^38+1306x^39+1137x^40+1494x^41+1177x^42+1030x^43+427x^44+328x^45+154x^46+64x^47+18x^48+12x^49+1x^50+1x^52

The gray image is a code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 0.406 seconds.