The generator matrix

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

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+161x^44+168x^45+392x^46+452x^47+659x^48+576x^49+582x^50+408x^51+346x^52+184x^53+104x^54+4x^55+22x^56+22x^58+8x^60+4x^62+1x^64+1x^68+1x^72

The gray image is a code over GF(2) with n=392, k=12 and d=176.
This code was found by Heurico 1.16 in 0.391 seconds.