The generator matrix

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

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+378x^40+488x^42+536x^44+248x^46+235x^48+120x^50+30x^52+8x^54+2x^56+2x^60

The gray image is a code over GF(2) with n=176, k=11 and d=80.
This code was found by Heurico 1.11 in 1.29 seconds.