The generator matrix

 1  0  0  1  1  1  X  1  1  2  1  1 X+2  0  2  1  1 X+2  1 X+2  1  1  1  1  0  X  1  1  1  1  0  2  1  X  2  X  1  1  1  1  1  X  1  1
 0  1  0  0  1  1  1  X X+3  1  X X+3  1  1 X+2  1  2  1 X+1  X X+3 X+2  X  X  0  1  0  3 X+1 X+3 X+2 X+2 X+2  2  1  1 X+1  2  1 X+1  1  1  0  0
 0  0  1 X+1 X+3  0  1  X  3  3  1  X X+3  X  1  1  1  2  0  1 X+2  0  1  2  1  X X+3 X+2 X+1  3  1  1  3  1  2  3 X+1 X+2 X+2 X+1 X+1 X+3  0  2
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  0  0  2  0  2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  2  2  0  2  2  0  0  2  2  2  0  0  2  0  2  2  0
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  2  0  2  0  2  0  2  0  2  0  2  2  2  0  0  0  0  0  0  0  0  2  2  0  0  2  2  2  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+48x^38+226x^39+273x^40+508x^41+476x^42+458x^43+369x^44+482x^45+262x^46+352x^47+218x^48+208x^49+104x^50+50x^51+31x^52+18x^53+6x^54+2x^55+4x^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 0.455 seconds.