The generator matrix

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

generates a code of length 54 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+380x^49+823x^50+1774x^51+1924x^52+2440x^53+2200x^54+2438x^55+1604x^56+1366x^57+678x^58+436x^59+164x^60+100x^61+8x^62+22x^63+19x^64+2x^65+3x^66+2x^67

The gray image is a code over GF(2) with n=432, k=14 and d=196.
This code was found by Heurico 1.16 in 2.13 seconds.