The generator matrix

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

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+89x^22+202x^23+512x^24+642x^25+1063x^26+940x^27+1267x^28+1050x^29+1112x^30+506x^31+469x^32+206x^33+67x^34+32x^35+23x^36+6x^37+5x^38

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 1.06 seconds.