The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+95x^22+244x^23+466x^24+714x^25+830x^26+1056x^27+1253x^28+1206x^29+970x^30+644x^31+378x^32+182x^33+86x^34+40x^35+11x^36+10x^37+3x^38+3x^40

The gray image is a linear code over GF(2) with n=112, k=13 and d=44.
This code was found by Heurico 1.16 in 0.973 seconds.