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
0 X 0 X^2+X 0 X^2+X 0 X 0 X^2+X 0 X 0 X^2+X X^2 X X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X 0 X^2 X^2+X X X^2 0
0 0 X^2 0 0 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2 0 X^2 X^2 X^2 X^2 X^2 0 0
0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 0
0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 0
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+31x^28+192x^30+31x^32+1x^60
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 0.0112 seconds.