The generator matrix
1 1 1 1 1 1 1 X X^3 X 1 X 1 1
0 X 0 X X^3 0 X^2+X X^2 X^3+X^2 X^2+X X^3+X^2+X X^3+X^2+X 0 X^3+X^2
0 0 X X X^2 X^2+X X^2+X X X 0 X^2 X^2 X^3 X^3
0 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 X^3 0
generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.
Homogenous weight enumerator: w(x)=1x^0+100x^11+150x^12+544x^13+480x^14+536x^15+127x^16+96x^17+4x^19+10x^20
The gray image is a linear code over GF(2) with n=112, k=11 and d=44.
This code was found by Heurico 1.16 in 0.016 seconds.