The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+112x^47+377x^48+578x^49+872x^50+1176x^51+1366x^52+1474x^53+1515x^54+1648x^55+1484x^56+1384x^57+1371x^58+1106x^59+824x^60+526x^61+285x^62+132x^63+70x^64+34x^65+19x^66+18x^67+6x^68+4x^69+2x^74

The gray image is a code over GF(2) with n=220, k=14 and d=94.
This code was found by Heurico 1.13 in 3.56 seconds.