The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+73x^24+46x^25+195x^26+248x^27+406x^28+532x^29+713x^30+1272x^31+1638x^32+2078x^33+2145x^34+1830x^35+1560x^36+1362x^37+850x^38+558x^39+367x^40+204x^41+170x^42+58x^43+50x^44+2x^45+21x^46+2x^47+1x^48+1x^50+1x^58

The gray image is a linear code over GF(2) with n=136, k=14 and d=48.
This code was found by Heurico 1.16 in 7.48 seconds.