The generator matrix
1 0 1 1 1 0 1 1 1 1 1 1 0 1
0 1 1 0 1 1 X+3 2 0 X+1 X+2 3 1 0
0 0 X 0 0 0 X 2 X+2 X+2 2 2 0 0
0 0 0 X 0 X+2 X 2 X 2 X+2 2 X+2 0
0 0 0 0 X 0 X+2 X 2 X+2 X+2 2 X+2 0
0 0 0 0 0 2 2 2 0 0 2 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+51x^8+74x^9+231x^10+396x^11+939x^12+1554x^13+1641x^14+1624x^15+964x^16+382x^17+225x^18+60x^19+29x^20+6x^21+15x^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 0.243 seconds.