The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+20x^40+110x^41+36x^42+96x^43+32x^44+102x^45+24x^46+48x^47+1x^48+10x^49+2x^50+16x^51+8x^52+2x^53+2x^56+1x^58+1x^74

The gray image is a code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 0.0356 seconds.