The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  1  1  1
 0 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0
 0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0 X^3 X^3  0  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  0 X^3 X^3  0  0
 0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0  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+38x^8+17x^10+52x^12+128x^13+1580x^14+128x^15+33x^16+54x^18+4x^20+12x^22+1x^26

The gray image is a linear code over GF(2) with n=112, k=11 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.