The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  0  X  2  0  0  0
 0  2  0  0  0  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2  0  2  2  0  0  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  2  2  2  2
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  2  2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  0  2  2  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+58x^44+1x^48+2x^52+2x^56

The gray image is a code over GF(2) with n=176, k=6 and d=88.
This code was found by Heurico 1.16 in 0.0287 seconds.