The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+58x^32+8x^33+123x^34+110x^35+222x^36+324x^37+484x^38+636x^39+901x^40+1230x^41+1419x^42+1788x^43+1737x^44+1736x^45+1506x^46+1272x^47+897x^48+724x^49+441x^50+262x^51+222x^52+68x^53+104x^54+28x^55+47x^56+6x^57+17x^58+10x^60+2x^62+1x^76

The gray image is a linear code over GF(2) with n=176, k=14 and d=64.
This code was found by Heurico 1.16 in 11.2 seconds.