The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+54x^27+175x^28+148x^29+184x^30+338x^31+505x^32+490x^33+370x^34+494x^35+452x^36+338x^37+186x^38+118x^39+134x^40+46x^41+22x^42+20x^43+13x^44+2x^45+6x^46

The gray image is a linear code over GF(2) with n=136, k=12 and d=54.
This code was found by Heurico 1.16 in 5.71 seconds.