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  1  1  X  0  2  X  X  X  2  0  2  1  0  X  X  1  0  1  X  0  1  1
 0  X  0  0  0  0  0  0  0  X X+2  X  X X+2  X  2  X  2  2 X+2  0  2 X+2  X  2  2  X  X  2  2  X  X  X  X  X X+2  X  2  0  X X+2  X  X  0
 0  0  X  0  0  0  X X+2  X  0  0  0  X  X X+2  2  X  X X+2  2 X+2  0  2 X+2  2  X  X  2  0  X X+2  0  0  0  X  X X+2  X  X X+2 X+2  2 X+2  0
 0  0  0  X  0  X  X X+2  0  X  X  2  0  2 X+2  X X+2  0 X+2 X+2  X X+2  X  2 X+2  0  X  2  X  X  0  X X+2  0  0  0 X+2  X X+2  0  0 X+2  2  X
 0  0  0  0  X  X  0 X+2  X  2 X+2 X+2  0 X+2  X  2  0  X  X  2  0 X+2 X+2 X+2  0  0 X+2  X  2  X  2  X X+2  2 X+2 X+2  2  X  X X+2  2  2  X  X
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  2  0  2  0  2  2  0  2  0  2  0  2  2  0  2  0  0  2  2  0  2
 0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  2  2  0  2  0  0  2  0  2  0  2  2  0  2  0  0  0  2  0  2  2  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  2  0  2  0  2  2  0  0  2  2  2  2  2  0  2  2  0  2  2  0  2  2  0  2  0  0  2  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+69x^34+136x^35+235x^36+330x^37+525x^38+700x^39+922x^40+1146x^41+1438x^42+1814x^43+1781x^44+1704x^45+1516x^46+1238x^47+931x^48+678x^49+457x^50+314x^51+207x^52+100x^53+87x^54+22x^55+18x^56+8x^57+3x^58+1x^60+2x^61+1x^74

The gray image is a code over GF(2) with n=176, k=14 and d=68.
This code was found by Heurico 1.16 in 11.6 seconds.