The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X^2 1 X^2
0 X 0 0 0 0 0 0 0 X X^2+X X X^2 X^2 X 0 X^2+X X^2+X X X^2+X X X X^2 X X X^2+X 0 X^2+X 0 X 0 X^2 X^2 X^2
0 0 X 0 0 0 X X^2+X X X X 0 0 X X^2 X X^2 X^2+X X^2+X 0 0 X X^2 X X^2+X X^2 X^2+X X^2 0 X^2+X X^2 X^2 X X^2
0 0 0 X 0 X X X X^2 0 0 X^2 X^2 X^2 X^2+X X^2+X X^2+X X 0 X^2+X X^2 X^2+X X^2+X 0 X 0 0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2
0 0 0 0 X X X^2 X^2+X X^2+X 0 X X 0 X^2+X X X^2 X^2+X X^2+X X 0 X^2 0 X^2 0 X X X^2 0 X^2+X X^2 X 0 X 0
0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 X^2 0 0 0
generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+480x^28+1534x^32+1664x^36+384x^40+32x^44+1x^64
The gray image is a linear code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 72.9 seconds.