The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  1  0  1
 0  1  0  0  X  1  1  1 X+1 X+1 X+1  0  1  X
 0  0  1  0 X+1  1  X X+1  1 X+1  0  X  X  0
 0  0  0  1  1  X X+1  1  1 X+1  X  X  X  1

generates a code of length 14 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+15x^10+36x^11+29x^12+26x^13+34x^14+42x^15+33x^16+20x^17+15x^18+1x^20+2x^21+2x^23

The gray image is a linear code over GF(2) with n=28, k=8 and d=10.
This code was found by Heurico 1.16 in 0.00138 seconds.