The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1  X  X  1  1 X+2  1  1  1  1 X+2  1  1  X  2  1  0  1  1  X  1  1  1  X  X  2  2  X  1 X+2  2
 0  1  1  0 X+1  1 X+3  0  1  3  1 X+3  2 X+2  1  1  1 X+2  1 X+3  X  3  0  1  3 X+2  1  1  0  1  X  2  1  1 X+3  2  2  1  X  X  1 X+2  1  X
 0  0  X  0  0  0  0  X  X X+2  X  2  X  X X+2  0  0  2  X X+2  X  2  2  0  X  X  0 X+2  X  0  0 X+2  0  2  0  X X+2  X  X X+2 X+2 X+2  X  X
 0  0  0  X  0 X+2 X+2  X  X  X  0  2  2 X+2  2 X+2  X  0  X  2  2  2  2  2  0  X  0  0  X  2 X+2  0  2 X+2  X  2 X+2 X+2  2 X+2  X  0  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  2  2  2  2  0  0  2  2  0  0  2  0  0  0  2  0  2  0  2  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  2  0  2  2  2  2  2  2  2  0  0  2  2
 0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  2  2  2  0  0  2  0  0  2  2  0  2  0  2  0  0  2  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  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+54x^35+161x^36+242x^37+495x^38+606x^39+1006x^40+1270x^41+1507x^42+1954x^43+1841x^44+1898x^45+1608x^46+1274x^47+944x^48+618x^49+432x^50+192x^51+133x^52+60x^53+49x^54+16x^55+8x^56+8x^57+5x^58+1x^60+1x^64

The gray image is a code over GF(2) with n=176, k=14 and d=70.
This code was found by Heurico 1.16 in 93.9 seconds.