The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+160x^40+964x^41+2971x^42+5934x^43+10037x^44+14820x^45+19874x^46+21478x^47+19703x^48+15336x^49+10547x^50+5400x^51+2355x^52+948x^53+364x^54+126x^55+30x^56+12x^57+4x^58+6x^59+2x^60

The gray image is a code over GF(2) with n=376, k=17 and d=160.
This code was found by Heurico 1.16 in 96.3 seconds.