The generator matrix

 1  1  1  1  1  1  X  1  1 X^2  X  X  X  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0  0  0
 0  0 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  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+39x^10+134x^12+602x^14+512x^15+591x^16+120x^18+42x^20+6x^22+1x^26

The gray image is a linear code over GF(2) with n=120, k=11 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.