The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  X  X  1  1  0  1  1  2 X^2  1  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2+2 X^2 X^2+X X^2+X  0 X+2 X^2+X+2 X^2 X^2+X+2 X+2  2 X^2+X+2 X^2+2  0  X X^2 X^2+X+2 X+2 X^2  X  X  2 X^2+X+2 X^2+X  0 X^2+2 X+2  X X^2+X+2  2  X X^2  2 X^2+X  2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  2  X X+2  0 X^2+X X^2+X+2 X^2+2  0 X^2+X+2 X^2  2  2 X^2+2  X X^2+X X^2 X^2  2 X+2 X+2 X^2+X+2 X^2+X  X X+2 X^2+X X^2  0 X+2 X+2 X+2 X^2+X X^2+X+2 X^2+X+2 X^2  X  0  X X+2
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  2  0  2  0  2  0  2  2  2  0  0  0  0  0  2  0  2  0  0  2  2  0  2  0  0

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+138x^43+108x^44+252x^45+343x^46+440x^47+338x^48+188x^49+94x^50+78x^51+8x^52+40x^53+3x^54+16x^55+1x^80

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 0.125 seconds.