The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+158x^41+642x^42+1918x^43+2605x^44+3878x^45+4449x^46+5462x^47+4662x^48+4242x^49+2211x^50+1382x^51+681x^52+306x^53+87x^54+52x^55+17x^56+8x^57+3x^58+2x^60+2x^63

The gray image is a code over GF(2) with n=376, k=15 and d=164.
This code was found by Heurico 1.16 in 7.2 seconds.