The generator matrix

 1  1  1  1  1  1  1  1  1  X X^2  1  1  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^3  0 X^2 X^2  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^2 X^3+X^2  0
 0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 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+21x^10+18x^11+48x^12+82x^13+574x^14+572x^15+571x^16+76x^17+38x^18+18x^19+20x^20+2x^21+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.