The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 X X 1 1 X^2 X^2 X X^2 X 1 X^3 X^3 X 1 0 0 X^2
0 X^3 0 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 X^3 X^3 0 X^3 X^3 0
0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 X^3 0 0 X^3 0 X^3 0 X^3 0
generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+56x^34+2x^36+4x^38+1x^48
The gray image is a linear code over GF(2) with n=272, k=6 and d=136.
This code was found by Heurico 1.16 in 0.141 seconds.