The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+96x^43+243x^44+152x^45+440x^46+160x^47+516x^48+144x^49+184x^50+64x^51+21x^52+24x^53+1x^56+2x^64

The gray image is a code over GF(2) with n=376, k=11 and d=172.
This code was found by Heurico 1.16 in 0.094 seconds.