The generator matrix
1 1 1 1 1 1 X X X 1 1 X X^2 X^2 X^2
0 X^3 0 X^3 0 0 X^3 X^3 0 X^3 X^3 0 0 X^3 0
0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3 0 0 X^3 X^3 0
generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+12x^14+32x^15+15x^16+4x^18
The gray image is a linear code over GF(2) with n=120, k=6 and d=56.
This code was found by Heurico 1.16 in -6.48e-008 seconds.