The generator matrix

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

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+573x^44+656x^45+768x^46+496x^47+671x^48+256x^49+328x^50+176x^51+115x^52+16x^53+32x^54+6x^56+2x^60

The gray image is a code over GF(2) with n=376, k=12 and d=176.
This code was found by Heurico 1.16 in 0.75 seconds.