The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+X  1  1  0  1  1  1  1  1  1  1  1 X^2  X X^2  X  1  1  1  1 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 X^2  X X^2+X+1  1 X^2  X X^2+X+1  1  1  1  1  1  0 X^2+X  0 X^2+X X^2  0
 0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 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+10x^28+52x^29+10x^30+40x^31+5x^32+4x^33+4x^34+2x^42

The gray image is a linear code over GF(2) with n=120, k=7 and d=56.
This code was found by Heurico 1.16 in 0.00668 seconds.