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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+66x^38+104x^40+50x^42+582x^44+112x^46+65x^48+6x^50+2x^52+20x^54+13x^56+2x^62+1x^72

The gray image is a code over GF(2) with n=176, k=10 and d=76.
This code was found by Heurico 1.16 in 34.5 seconds.