The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 1
0 X^2 0 0 0 0 0 0 0 0 0 0 X^2 0
0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 0
0 0 0 X^2 0 0 0 0 0 0 0 0 X^2 0
0 0 0 0 X^2 0 0 0 0 0 0 0 X^2 0
0 0 0 0 0 X^2 0 0 0 0 0 0 X^2 0
0 0 0 0 0 0 X^2 0 0 0 0 0 X^2 0
0 0 0 0 0 0 0 X^2 0 0 0 0 X^2 0
0 0 0 0 0 0 0 0 X^2 0 0 0 X^2 0
0 0 0 0 0 0 0 0 0 X^2 0 0 X^2 0
0 0 0 0 0 0 0 0 0 0 X^2 0 X^2 0
0 0 0 0 0 0 0 0 0 0 0 X^2 X^2 0
generates a code of length 14 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+66x^4+12x^6+495x^8+220x^10+924x^12+2048x^13+8984x^14+2048x^15+495x^16+792x^18+66x^20+220x^22+1x^24+12x^26
The gray image is a linear code over GF(2) with n=56, k=14 and d=8.
This code was found by Heurico 1.16 in 0.342 seconds.