The generator matrix

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

generates a code of length 15 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+162x^11+1055x^12+2782x^13+7268x^14+10132x^15+7485x^16+2748x^17+916x^18+170x^19+43x^20+6x^21

The gray image is a linear code over GF(2) with n=120, k=15 and d=44.
This code was found by Heurico 1.16 in 1.89 seconds.