The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+44x^36+88x^37+214x^38+390x^39+486x^40+638x^41+839x^42+970x^43+997x^44+946x^45+788x^46+610x^47+455x^48+310x^49+180x^50+102x^51+58x^52+30x^53+26x^54+8x^55+6x^56+4x^57+1x^58+1x^60

The gray image is a code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 2.5 seconds.