The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  1  1  1
 0  1  1  0  1  1 X+1  0  1  X  3  X X+3 X+3
 0  0  X  0  0  0  0  X  2  X  X  X X+2  X
 0  0  0  X  0 X+2  X  X  2  0  2 X+2 X+2  0
 0  0  0  0  X  0  X  2 X+2  2  X X+2  X  0
 0  0  0  0  0  2  0  0  2  2  0  0  2  2
 0  0  0  0  0  0  2  2  0  0  2  2  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+76x^8+138x^9+282x^10+944x^11+1326x^12+4010x^13+2790x^14+4080x^15+1291x^16+958x^17+310x^18+96x^19+58x^20+14x^21+10x^22

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 0.749 seconds.