The generator matrix
1 0 1 1 1 X^2 1 1 0 1 1 0 X 1 1 1 1 0 1 1 X X X^2+X 1 1 1 1 1 1 1
0 1 1 0 X+1 1 1 0 1 X^2 X+1 1 1 X^2+1 X^2+X X X+1 1 X X 1 1 1 X^2+X 0 X^2+1 X+1 1 0 X
0 0 X 0 0 X^2 0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2 0 X^2 0 X^2 X^2+X X X X^2+X X^2 X 0 X X X X^2 X^2+X
0 0 0 X X^2 X X^2+X X^2+X X^2+X X^2 X X^2 X^2+X X^2 0 X X^2+X 0 X^2 X^2+X X^2+X X^2 X^2 X X^2 X^2+X X^2 X 0 0
generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+51x^26+130x^27+165x^28+148x^29+96x^30+114x^31+145x^32+100x^33+37x^34+10x^35+9x^36+8x^37+6x^38+2x^39+2x^42
The gray image is a linear code over GF(2) with n=120, k=10 and d=52.
This code was found by Heurico 1.16 in 0.0278 seconds.