The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 0 1 X^2 1 X^2+X X^2+X X 0 X 0 X X^2 X 1
0 1 X+1 X^2+X 1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2 1 X^2+X+1 1 1 1 X 1 1 0 1 X^2+X 0
0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 0 0
0 0 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 X^2 0 0
0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0
generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+23x^24+76x^25+32x^26+124x^27+20x^28+116x^29+29x^30+52x^31+18x^32+16x^33+1x^34+2x^36+1x^38+1x^50
The gray image is a linear code over GF(2) with n=112, k=9 and d=48.
This code was found by Heurico 1.16 in 0.0106 seconds.