The generator matrix
1 0 1 1 1 3X+2 1 1 2 1 1 3X+2 X X
0 1 X+1 3X+2 2X+3 1 2 X+3 1 3X 2X+1 1 0 0
0 0 2X 0 0 0 0 2X 0 2X 2X 2X 0 0
0 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X
0 0 0 0 2X 0 2X 0 2X 2X 2X 2X 2X 0
0 0 0 0 0 2X 0 2X 2X 2X 0 2X 2X 0
generates a code of length 14 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+46x^10+64x^11+326x^12+1216x^13+806x^14+1216x^15+303x^16+64x^17+42x^18+10x^20+2x^22
The gray image is a code over GF(2) with n=112, k=12 and d=40.
This code was found by Heurico 1.16 in 0.032 seconds.