The generator matrix
1 1 1 1 1 1 1 1 X X X^3+X^2 X^2 X^3+X^2 1
0 X 0 X X^3 0 X^2+X X^3+X^2+X X^2 X X 0 X X^2
0 0 X X 0 X^3+X^2+X X^2+X X^3 X X^2+X X^2 0 X^2+X X^2
0 0 0 X^2 X^3+X^2 X^2 X^3 X^2 0 X^2 X^2 X^3+X^2 0 X^3
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+42x^10+168x^11+528x^12+802x^13+1040x^14+784x^15+519x^16+156x^17+38x^18+8x^19+8x^20+2x^21
The gray image is a linear code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.047 seconds.