The generator matrix

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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+357x^50+958x^51+1565x^52+2128x^53+2288x^54+2376x^55+2262x^56+1704x^57+1173x^58+802x^59+429x^60+180x^61+82x^62+36x^63+31x^64+4x^65+4x^66+2x^67+2x^75

The gray image is a code over GF(2) with n=440, k=14 and d=200.
This code was found by Heurico 1.16 in 2.19 seconds.