The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+86x^35+438x^36+1090x^37+1927x^38+2562x^39+3609x^40+5074x^41+6485x^42+7398x^43+7747x^44+7754x^45+6628x^46+5238x^47+3833x^48+2546x^49+1600x^50+812x^51+358x^52+172x^53+125x^54+32x^55+13x^56+4x^57+3x^58+1x^60

The gray image is a code over GF(2) with n=176, k=16 and d=70.
This code was found by Heurico 1.13 in 36.2 seconds.