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.