The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X X X X 2 2 2 0 0 0 1 X 1 X X X 1 1 X 2 1
0 2 0 2 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 2 2 0 0 0 0 2 2 0 2 2 0 0 0
0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 2 2 0 0 0 0
generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+3x^44+22x^45+3x^46+2x^49+1x^50
The gray image is a code over GF(2) with n=176, k=5 and d=88.
This code was found by Heurico 1.16 in 0.0253 seconds.