The generator matrix

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

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+150x^13+212x^14+356x^15+143x^16+120x^17+28x^18+12x^19+2x^21

The gray image is a linear code over GF(2) with n=120, k=10 and d=52.
This code was found by Heurico 1.16 in 0.031 seconds.