The generator matrix

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

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+102x^22+294x^23+532x^24+638x^25+842x^26+1128x^27+1154x^28+1072x^29+842x^30+726x^31+509x^32+206x^33+102x^34+28x^35+6x^36+4x^37+6x^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 0.829 seconds.