The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  2  1
 0  X  0  0  0  X X+2  X  2  2  0  X  X  0
 0  0  X  0  X  X X+2  0  0  2  X  0  X  0
 0  0  0  X  X  0 X+2  X  X X+2  X  X  2  0
 0  0  0  0  2  0  0  2  0  0  2  0  2  0
 0  0  0  0  0  2  0  2  0  2  2  2  2  0
 0  0  0  0  0  0  2  2  2  0  0  0  2  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+59x^8+60x^9+119x^10+344x^11+213x^12+1100x^13+251x^14+1200x^15+192x^16+308x^17+133x^18+56x^19+47x^20+4x^21+9x^22

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0512 seconds.