The generator matrix

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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+288x^49+898x^50+1742x^51+2886x^52+3940x^53+4106x^54+5110x^55+4442x^56+3962x^57+2610x^58+1356x^59+781x^60+404x^61+120x^62+78x^63+17x^64+10x^65+8x^66+2x^67+4x^69+2x^70+1x^76

The gray image is a code over GF(2) with n=440, k=15 and d=196.
This code was found by Heurico 1.16 in 7.84 seconds.