The generator matrix

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

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+280x^10+1688x^11+5664x^12+14866x^13+20392x^14+15160x^15+5611x^16+1532x^17+304x^18+32x^19+4x^20+2x^21

The gray image is a linear code over GF(2) with n=112, k=16 and d=40.
This code was found by Heurico 1.16 in 4.66 seconds.