The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2  1
 0  1 X+1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X X+1 X^2+1 X^2  X X^2+X+1  1  0 X^2  X  X X^2 X^2+X X^2  1  1  0
 0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0
 0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 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+71x^28+32x^29+48x^30+32x^31+70x^32+1x^44+1x^48

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 0.00817 seconds.