The generator matrix

 1  1  1  1  1  1  X  0  1  1  X  1  1  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^2+X  X X^3+X^2  X X^3  0 X^3+X^2+X X^3+X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^3  0 X^3+X^2 X^2  0 X^3+X^2 X^3 X^3
 0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+38x^12+80x^13+217x^14+364x^15+226x^16+56x^17+20x^18+12x^19+6x^20+3x^22+1x^24

The gray image is a linear code over GF(2) with n=120, k=10 and d=48.
This code was found by Heurico 1.16 in 6.87e-008 seconds.