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.