The generator matrix

 1  0  0  1  1  1 X+2  1  1 X+2 X+2  1  1  0  1  1  1  1  X  0  1  2  2  1  1  0  1  2  X  1  0  1  1  1  1  1  1  1  1  1 X+2 X+2  2  2
 0  1  0  0  1 X+1  1  2  0  2  1  3  3  1 X+2  1  X  3  0  1 X+2  1 X+2 X+1  2  1  X  1  1  0  1 X+3 X+3 X+3  X X+3  1  3  X X+1  1  1  1  1
 0  0  1  1  1  0 X+1  X X+3  1  0  2 X+1 X+1  2 X+1  1 X+2  1 X+1  0  0  1  2  X  3  X  3  2 X+1 X+1 X+2 X+1  3 X+3  1 X+3 X+2  1 X+1  X  0 X+2  2
 0  0  0  X  0  2  0  2 X+2  0  2  0  0  0  0  X  2 X+2 X+2 X+2  X  X X+2 X+2  X X+2  X  2  X  2  X  0 X+2  2 X+2  2  2  2  0 X+2  X  0  0 X+2
 0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  2  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  2  0  2  2  2  2  2  0  2

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+71x^38+188x^39+326x^40+436x^41+484x^42+428x^43+425x^44+488x^45+358x^46+236x^47+214x^48+220x^49+124x^50+44x^51+19x^52+8x^53+19x^54+7x^56

The gray image is a code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 0.462 seconds.