The generator matrix

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

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+140x^36+48x^37+204x^38+208x^39+648x^40+496x^41+936x^42+784x^43+1285x^44+784x^45+976x^46+496x^47+597x^48+208x^49+184x^50+48x^51+102x^52+4x^54+34x^56+9x^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 2.42 seconds.