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.