The generator matrix
1 1 1 1 1 1 1 1 X X 1 1 X 1
0 X^3+X^2 0 0 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2 0 X^3 0 0
0 0 X^3+X^2 0 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 0 0 X^2
0 0 0 X^3+X^2 X^2 X^3 X^2 X^2 0 X^3 X^3 X^2 X^3+X^2 X^2
generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+19x^10+34x^11+44x^12+98x^13+637x^14+92x^15+51x^16+28x^17+13x^18+2x^19+2x^21+3x^22
The gray image is a linear code over GF(2) with n=112, k=10 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.