The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  1  X  1  0 X^2  1  X  X  1  X  0  X  1  0  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2  X X^2+X X^2  0  X X^2+X X^2  0  X X^2 X^2  X  0  0  0 X^2+X X^2+X  X  X  X  0 X^2  X  0
 0  0  X  0  X  X X^2+X  0  0  0  0 X^2 X^2+X  X  X X^2+X  X X^2+X  X  0 X^2+X  X  X X^2+X X^2+X  X  0 X^2  0  0 X^2  0  X  0
 0  0  0  X  X  0 X^2+X  X  0  X X^2+X X^2  X  X  0 X^2  0  0  X  X X^2+X  X X^2+X  0 X^2 X^2+X X^2+X X^2+X  0 X^2+X X^2  X  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  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  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  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  0 X^2  0  0  0  0 X^2 X^2  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+84x^24+70x^25+196x^26+218x^27+452x^28+576x^29+841x^30+1250x^31+1531x^32+1892x^33+1932x^34+2028x^35+1544x^36+1384x^37+935x^38+540x^39+448x^40+166x^41+156x^42+58x^43+36x^44+8x^45+31x^46+2x^47+4x^50+1x^54

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 7.43 seconds.