The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+48x^28+58x^29+69x^30+28x^31+30x^32+10x^33+10x^34+1x^36+1x^50

The gray image is a linear code over GF(2) with n=120, k=8 and d=56.
This code was found by Heurico 1.16 in 0.0079 seconds.