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^2  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2
 0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2

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+15x^28+224x^30+15x^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 0.00961 seconds.