The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+32x^34+66x^35+167x^36+236x^37+452x^38+612x^39+971x^40+1286x^41+1542x^42+1912x^43+1837x^44+1892x^45+1635x^46+1260x^47+947x^48+632x^49+388x^50+230x^51+153x^52+48x^53+39x^54+16x^55+17x^56+2x^57+6x^58+3x^60+1x^62+1x^70

The gray image is a linear code over GF(2) with n=176, k=14 and d=68.
This code was found by Heurico 1.16 in 8.6 seconds.