The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  1  1  1
 0  1  1  0 X+1  1  0 X+1  1  X  3 X+2 X+3  0
 0  0  X  0  X  0  X  0  X X+2  0 X+2  2  0
 0  0  0  X  X X+2  X  0  0  2  2 X+2 X+2  0
 0  0  0  0  2  0  0  0  2  0  2  2  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  2  0  0  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+58x^8+70x^9+202x^10+436x^11+920x^12+1530x^13+1738x^14+1560x^15+909x^16+442x^17+222x^18+52x^19+32x^20+6x^21+14x^22

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 0.203 seconds.