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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+130x^32+317x^36+32x^38+556x^40+480x^42+5150x^44+480x^46+600x^48+32x^50+279x^52+116x^56+13x^60+5x^64+1x^76

The gray image is a code over GF(2) with n=176, k=13 and d=64.
This code was found by Heurico 1.16 in 4.06 seconds.