The generator matrix
1 1 1 1 1 1 1 1 1 X X 2 1 X
0 X 0 X 0 0 X X+2 2 2 X X X X+2
0 0 X X 0 X+2 X 2 0 X X X+2 X 0
0 0 0 2 0 0 2 0 0 2 0 2 0 2
0 0 0 0 2 0 0 2 2 2 0 0 0 2
0 0 0 0 0 2 2 0 2 0 0 2 2 2
generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+62x^10+16x^11+198x^12+112x^13+262x^14+112x^15+175x^16+16x^17+58x^18+10x^20+2x^22
The gray image is a code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 0.126 seconds.