The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+125x^8+576x^10+1024x^11+1656x^12+3072x^13+3456x^14+3072x^15+1691x^16+1024x^17+576x^18+104x^20+7x^24

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.475 seconds.