The generator matrix

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

generates a code of length 49 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+224x^46+460x^47+285x^48+196x^49+236x^50+412x^51+183x^52+12x^53+16x^54+8x^55+8x^56+4x^58+1x^60+1x^64+1x^72

The gray image is a code over GF(2) with n=392, k=11 and d=184.
This code was found by Heurico 1.16 in 0.094 seconds.