The generator matrix

 1  1  1  1  1  1  1  1  X  1 X^3  1  X  X  1
 0  X  0 X^3+X^2+X  0 X^2+X  0  X X^2+X X^3  X X^3+X^2+X X^2+X X^3+X^2  0
 0  0 X^3+X^2  0  0 X^2 X^3+X^2 X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^2  0
 0  0  0 X^3+X^2 X^3+X^2 X^2 X^2  0 X^2 X^3 X^3+X^2 X^3 X^2 X^2  0
 0  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  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+36x^10+72x^11+129x^12+342x^13+603x^14+1720x^15+605x^16+372x^17+122x^18+48x^19+33x^20+6x^21+7x^22

The gray image is a linear code over GF(2) with n=120, k=12 and d=40.
This code was found by Heurico 1.16 in 0.046 seconds.