The generator matrix
1 0 0 1 1 1 0 1 1 X 1 1 1 1 1
0 1 0 1 X X+1 1 0 X 0 1 0 X+1 X 0
0 0 1 1 1 0 X+1 X X+1 1 X+1 X 1 X 0
0 0 0 X 0 X X X X X 0 0 0 0 X
generates a code of length 15 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+15x^12+24x^13+16x^14+24x^15+21x^16+8x^17+4x^18+8x^19+3x^20+4x^22
The gray image is a linear code over GF(2) with n=30, k=7 and d=12.
As d=12 is an upper bound for linear (30,7,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 7.
This code was found by Heurico 1.16 in 0.00107 seconds.