The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0
 0  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+38x^32+440x^34+24x^36+8x^38+1x^64

The gray image is a linear code over GF(2) with n=272, k=9 and d=128.
This code was found by Heurico 1.16 in 0.141 seconds.