The generator matrix

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

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+94x^8+100x^9+209x^10+288x^11+444x^12+1636x^13+2604x^14+1696x^15+425x^16+300x^17+246x^18+64x^19+60x^20+12x^21+12x^22+1x^26

The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.278 seconds.