The generator matrix

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

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+14x^10+8x^11+29x^12+32x^13+89x^14+688x^15+82x^16+32x^17+21x^18+8x^19+15x^20+3x^22+1x^24+1x^26

The gray image is a linear code over GF(2) with n=120, k=10 and d=40.
This code was found by Heurico 1.16 in 3.62e-008 seconds.