The generator matrix

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

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+190x^10+1548x^11+6603x^12+24640x^13+58164x^14+79692x^15+58374x^16+24736x^17+6510x^18+1444x^19+205x^20+32x^21+4x^23+1x^24

The gray image is a linear code over GF(2) with n=120, k=18 and d=40.
This code was found by Heurico 1.16 in 66.7 seconds.