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  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2
 0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  2  0  0  0  0  2  2  0  0  2  2  0  2  2  2
 0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0
 0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  0  2  0  0

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+7x^42+30x^43+72x^44+8x^46+7x^48+1x^58+2x^59

The gray image is a code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in 0.0268 seconds.