The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+122x^41+656x^42+1548x^43+2766x^44+3924x^45+4953x^46+5020x^47+5178x^48+3756x^49+2507x^50+1340x^51+562x^52+232x^53+127x^54+40x^55+11x^56+14x^57+5x^58+4x^59+2x^60

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 6.8 seconds.