The generator matrix

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

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+176x^27+124x^28+280x^29+64x^30+144x^31+31x^32+96x^33+64x^35+36x^36+8x^37

The gray image is a linear code over GF(2) with n=120, k=10 and d=54.
This code was found by Heurico 1.16 in 15.4 seconds.