The generator matrix

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

generates a code of length 55 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+189x^48+228x^49+566x^50+532x^51+760x^52+696x^53+848x^54+744x^55+836x^56+652x^57+746x^58+468x^59+346x^60+208x^61+218x^62+48x^63+62x^64+8x^65+16x^66+14x^68+6x^70

The gray image is a code over GF(2) with n=220, k=13 and d=96.
This code was found by Heurico 1.16 in 2.87 seconds.