The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  2  1 X+2  1  1  0  1  2  1  1  X  1  1  1  0  1  1  0  1  1 X+2  1  1  2  1  1 X+2  1  1  0  1  1  1
 0  1  1  0  1  1  0 X+1  1 X+2 X+1  1 X+3  1  2  0  1  3  1 X+1  0  1 X+2  2  1  1 X+2 X+3  1  3  1  1  X  0  1  1 X+2  1 X+3 X+3  X  0  2  0
 0  0  X  0  0  0  0  X  0  0 X+2  2 X+2  2  X  X  X  2  X  2 X+2 X+2  X  X X+2  X  0 X+2  X  0  0  0  0  2  0  2  2 X+2  0 X+2  0  2  2  2
 0  0  0  X  0  0  0  0  2 X+2 X+2 X+2  X X+2  2  X  X  X X+2  2  0  2  X  0  0  2  2 X+2  2 X+2  X  2  2  0 X+2  2 X+2 X+2 X+2 X+2  2  X  2  2
 0  0  0  0  X X+2 X+2  X X+2 X+2  2  0 X+2  X  0  0  2  0  X  0 X+2  2  2  0 X+2  0  0  2 X+2 X+2  X  0 X+2  2  X  2  X  X X+2  2  X  0 X+2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  2  2  2  0  2  0  2  2  2  0  2  2  2
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0  0  2  0  2  0  0  2  0  0  2  0  0  0  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+42x^35+139x^36+248x^37+415x^38+614x^39+921x^40+1298x^41+1623x^42+1866x^43+1997x^44+1956x^45+1655x^46+1306x^47+909x^48+600x^49+374x^50+180x^51+119x^52+52x^53+25x^54+24x^55+9x^56+6x^57+3x^58+1x^60+1x^62

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 9.13 seconds.