The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1
0 X^2 0 0 0 0 0 0 0 0 0 0
0 0 X^2 0 0 0 0 0 0 0 0 0
0 0 0 X^2 0 0 0 0 0 0 0 0
0 0 0 0 X^2 0 0 0 0 0 0 0
0 0 0 0 0 X^2 0 0 0 0 0 0
0 0 0 0 0 0 X^2 0 0 0 0 0
0 0 0 0 0 0 0 X^2 0 0 0 0
0 0 0 0 0 0 0 0 X^2 0 0 0
0 0 0 0 0 0 0 0 0 X^2 0 0
0 0 0 0 0 0 0 0 0 0 X^2 0
0 0 0 0 0 0 0 0 0 0 0 X^2
generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+12x^2+66x^4+220x^6+495x^8+792x^10+13212x^12+792x^14+495x^16+220x^18+66x^20+12x^22+1x^24
The gray image is a linear code over GF(2) with n=48, k=14 and d=4.
This code was found by Heurico 1.16 in 0.154 seconds.