The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  1  1
 0 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0
 0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0
 0  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0
 0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0
 0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0  0
 0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+26x^8+68x^12+832x^14+73x^16+20x^20+4x^24

The gray image is a linear code over GF(2) with n=112, k=10 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.