The generator matrix
1 0 1 1 1 0 1 X 1 X 1 1 0 2
0 1 1 0 X+1 1 X X X+2 2 X+3 3 1 1
0 0 X X+2 0 X+2 X X 0 X X 0 0 X
0 0 0 2 0 0 0 0 0 2 0 2 0 2
0 0 0 0 2 0 0 0 0 0 0 2 2 2
0 0 0 0 0 2 0 0 0 0 2 2 2 0
0 0 0 0 0 0 2 0 0 2 0 2 2 0
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 0 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+125x^8+576x^10+1024x^11+1656x^12+3072x^13+3456x^14+3072x^15+1691x^16+1024x^17+576x^18+104x^20+7x^24
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 0.475 seconds.