The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2+2  1  1  1  1  1  1  X  1  1  1  1  1 X^2 X^2+2  X X^2+2  1  1 X^2+2  1  2  1  2  1  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+X+2 X^2+2  X X^2+2 X^2+X X^2+X+2  2  2 X^2+X+2  X  X X^2+X+2  X X^2 X^2+X+2 X^2+X+2 X^2+X X^2+X X+2 X^2+2 X^2+X+2  2 X^2+X  X  X  0 X^2 X^2+2 X^2+2  X  X X^2 X+2  2  X  2
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2 X^2  X  X X^2+X+2 X+2  X X+2 X^2+2 X^2+2  2 X^2+2  0 X^2+2 X^2+X X^2+X X^2+2 X^2 X^2+X+2 X^2 X+2 X^2+X X^2  X X^2+X+2  X X^2+X  X X^2 X^2 X^2+X X^2+X  X X^2+X  X  X X^2
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0  0 X^2+2  2 X^2 X^2+2  2 X^2  2  0 X^2 X^2+2  2 X^2  0 X^2  2 X^2+2  0  2 X^2 X^2+2 X^2+2  0 X^2+2 X^2  2 X^2  0 X^2  0  2  2 X^2+2 X^2+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+92x^44+268x^45+297x^46+426x^47+697x^48+750x^49+588x^50+360x^51+238x^52+160x^53+98x^54+60x^55+26x^56+22x^57+8x^58+2x^60+2x^63+1x^78

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 0.297 seconds.