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 1 1 1 1 1 X 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 2X 2X 2X 0 2X 0 0 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 0 2X 2X 0 2X 0 0 2X 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 0 2X
0 0 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 0 2X 0 2X 0 2X 0 0 0 2X 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 2X 0
0 0 0 2X 0 0 0 0 2X 0 0 2X 0 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 0
0 0 0 0 2X 0 0 0 2X 0 2X 2X 2X 0 0 2X 2X 0 0 2X 2X 2X 2X 2X 0 0 0 2X 0 2X 0 0 0 0 0 2X 2X 0 0 2X 0 2X 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 0 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X 2X 0 0 0 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 0 2X
0 0 0 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 2X 2X 0 0 2X 0 0
0 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 0 0 2X 2X 0 2X 2X 0 0 0 0 0 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0 2X 2X 0 0 0 0 0 0 2X 2X 2X
generates a code of length 55 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+67x^48+94x^52+96x^54+1536x^55+139x^56+32x^58+40x^60+32x^64+10x^68+1x^104
The gray image is a code over GF(2) with n=440, k=11 and d=192.
This code was found by Heurico 1.16 in 0.203 seconds.