The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+28x^10+16x^11+123x^12+176x^13+587x^14+544x^15+1155x^16+1872x^17+2189x^18+2976x^19+2206x^20+1872x^21+1182x^22+544x^23+586x^24+176x^25+102x^26+16x^27+23x^28+7x^30+2x^32+1x^34

The gray image is a linear code over GF(2) with n=76, k=14 and d=20.
This code was found by Heurico 1.16 in 1.05 seconds.