The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+46x^14+16x^15+201x^16+192x^17+400x^18+352x^19+396x^20+192x^21+184x^22+16x^23+38x^24+8x^26+4x^28+2x^30

The gray image is a linear code over GF(2) with n=76, k=11 and d=28.
This code was found by Heurico 1.16 in 0.13 seconds.