The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+378x^43+713x^44+1460x^45+1078x^46+1508x^47+904x^48+956x^49+460x^50+446x^51+119x^52+96x^53+46x^54+20x^55+7x^56

The gray image is a code over GF(2) with n=376, k=13 and d=172.
This code was found by Heurico 1.16 in 0.484 seconds.