The generator matrix

 1  0  0  0  1  1  1 X^2  1  X  1  0  1  1  0 X^2+X  1 X^2+X  0  1  1  X  1  1  1  0  1  1
 0  1  0  0  0  1 X^2+1  1 X^2+X  1 X^2  1 X^2+X+1 X^2+1 X^2+X  1  1  1  1  0 X^2+1  1 X^2 X^2+1  X  X X^2+1 X^2+X
 0  0  1  0  1  1 X^2  1 X^2 X^2+X  1 X+1 X^2+1  X  1 X^2+X+1  X X^2+X+1 X^2+X X^2 X+1 X^2+1  1 X^2+X+1 X^2+X+1  1  0  0
 0  0  0  1  1 X^2  1 X^2+1 X^2+1  1 X^2 X^2+X X^2+X+1  0 X+1 X^2+X+1  0 X^2+X X^2  X X^2+X  X X^2+X+1 X^2+X+1 X^2 X^2+X  1 X^2
 0  0  0  0  X  0  0  X  X  X X^2+X X^2+X  X X^2 X^2+X X^2 X^2+X  0  X X^2+X  X X^2+X X^2  0 X^2  0 X^2+X 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+188x^22+448x^23+1101x^24+1256x^25+1866x^26+2064x^27+2349x^28+2276x^29+2038x^30+1248x^31+926x^32+336x^33+190x^34+48x^35+39x^36+4x^37+6x^38

The gray image is a linear code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.13 in 1.27 seconds.