The generator matrix

 1  0  0  1  1  1  2  1  1 X^2+2  1  X X^2+X+2  1 X^2+X  1  1 X^2+X  1  X  1  0  1  1  1  1  2  X X^2  1  1  1  1 X^2+2  0  1 X^2+X X^2+X+2  1  0  1  X  X  1  1  X  1 X+2  1
 0  1  0  0 X^2+3 X^2+3  1  X X+3  X X^2  1  1 X^2+1 X+2  2 X^2+X+3  1 X^2+X  1 X+1  1 X^2+X X^2+X+2 X^2+X+3 X+3  1 X^2+2  2 X^2 X^2+X+1  3 X^2+1  1  1  1  1  1  X  1 X^2+X+3 X^2  1  X X^2+1  1 X^2+3  2  0
 0  0  1 X+1 X+1 X^2 X+1 X^2+3 X+3  1 X^2+X+2 X^2+1 X+2 X^2+X  1 X^2+1 X^2+1 X^2  X X+1  0 X^2+1 X+1 X^2 X^2+X+3 X+2 X+2  1  1  0  2 X^2+X+2  2 X^2+X+2 X+1 X^2+X+3  3  X X^2 X^2+X+3 X^2+X+2  1 X+1  2 X^2+X+1  0  0  1 X^2+X+2
 0  0  0 X^2 X^2+2  0 X^2+2 X^2+2 X^2+2 X^2  2 X^2  2  0 X^2 X^2  2 X^2 X^2  2  2 X^2+2  0 X^2+2 X^2 X^2 X^2  0 X^2+2 X^2 X^2+2 X^2 X^2+2 X^2+2  2  0  0 X^2+2 X^2 X^2 X^2+2 X^2 X^2  0 X^2  0  2  2  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+233x^44+770x^45+1641x^46+2198x^47+2525x^48+2288x^49+2297x^50+1802x^51+1330x^52+742x^53+321x^54+102x^55+75x^56+24x^57+19x^58+10x^59+3x^60+2x^62+1x^64

The gray image is a code over GF(2) with n=392, k=14 and d=176.
This code was found by Heurico 1.16 in 1.88 seconds.