The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+19x^34+62x^35+121x^36+200x^37+184x^38+472x^39+247x^40+924x^41+339x^42+1468x^43+295x^44+1336x^45+286x^46+912x^47+247x^48+544x^49+149x^50+150x^51+91x^52+64x^53+40x^54+8x^55+17x^56+4x^57+5x^58+5x^60+2x^62

The gray image is a code over GF(2) with n=176, k=13 and d=68.
This code was found by Heurico 1.16 in 3.21 seconds.