The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+28x^18+8x^19+89x^20+72x^21+140x^22+352x^23+498x^24+1504x^25+1362x^26+3184x^27+1890x^28+3184x^29+1384x^30+1504x^31+516x^32+352x^33+128x^34+72x^35+69x^36+8x^37+28x^38+8x^40+2x^42+1x^48

The gray image is a linear code over GF(2) with n=112, k=14 and d=36.
This code was found by Heurico 1.16 in 3.16 seconds.