The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0  1  1  1  1  1  1  X  1  X  1  1  1  2  X  1  X  1  2  1  2  1  1  1  1  2  1  1  X  1
 0  X  0  0  0  0  0  2  2  X X+2  X  X  X X+2  X  0 X+2  2  X  2  X  0  2  X  X  2  0 X+2  0  X  X  X  2 X+2 X+2  0  0  2  2 X+2  0  0  X  X  X X+2 X+2  X  0  X  X  2  0  0
 0  0  X  0  0  2 X+2  X  X  X  X  X X+2  0  0  0  2  2 X+2  X  2  0  0  X  X X+2  2 X+2  0 X+2 X+2  2 X+2  0  X  2  X X+2  0  0  0  2  0  0  2  2  X  2 X+2  0  X  X X+2  0  2
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  0  X  X  2  X  2 X+2  0 X+2  0  2  0  X  X  0  2 X+2  2  2  X  X  2  0  X  X  2  X X+2 X+2  X  X X+2  X  X  X X+2 X+2 X+2  2  X  0 X+2  X
 0  0  0  0  X  X  2 X+2  X X+2  2  2  X  2 X+2  X  X  2  2 X+2  0 X+2  0  0  0  0  X X+2  2  0  0  X X+2  2 X+2  2 X+2  X  X X+2  X  0  2  0  0 X+2 X+2  2  0  X  0  2  0  0  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+43x^48+88x^49+98x^50+104x^51+183x^52+258x^53+223x^54+218x^55+191x^56+166x^57+149x^58+94x^59+62x^60+46x^61+33x^62+22x^63+24x^64+18x^65+9x^66+10x^67+7x^68+1x^88

The gray image is a code over GF(2) with n=220, k=11 and d=96.
This code was found by Heurico 1.16 in 0.298 seconds.