The generator matrix

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

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+94x^10+914x^11+3369x^12+11590x^13+29042x^14+40996x^15+29074x^16+11708x^17+3338x^18+810x^19+99x^20+30x^21+6x^22+1x^24

The gray image is a linear code over GF(2) with n=120, k=17 and d=40.
This code was found by Heurico 1.16 in 16.9 seconds.