The generator matrix

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

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+95x^44+146x^46+96x^47+161x^48+1088x^49+132x^50+96x^51+132x^52+74x^54+26x^56+1x^92

The gray image is a code over GF(2) with n=392, k=11 and d=176.
This code was found by Heurico 1.16 in 0.141 seconds.