The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+72x^27+100x^28+76x^29+76x^30+48x^31+56x^32+40x^33+12x^34+8x^35+10x^36+12x^37+1x^40

The gray image is a linear code over GF(2) with n=120, k=9 and d=54.
This code was found by Heurico 1.16 in 0.0589 seconds.