The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^37+381x^38+614x^39+691x^40+578x^41+675x^42+524x^43+339x^44+106x^45+11x^46+22x^47+8x^48+12x^49+4x^50+2x^57+1x^58+1x^60

The gray image is a code over GF(2) with n=328, k=12 and d=148.
This code was found by Heurico 1.16 in 0.156 seconds.