The generator matrix

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

generates a code of length 43 over Z2[X]/(X^3) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+79x^34+244x^35+461x^36+922x^37+1268x^38+1824x^39+2574x^40+3080x^41+3781x^42+4038x^43+3892x^44+3432x^45+2607x^46+1854x^47+1185x^48+708x^49+378x^50+222x^51+107x^52+46x^53+45x^54+10x^55+4x^56+4x^57+2x^58

The gray image is a linear code over GF(2) with n=172, k=15 and d=68.
This code was found by Heurico 1.16 in 25.6 seconds.