The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 2 X X X
0 2X+2 0 2 0 2X 2X+2 2X+2 0 2X 0 0 2 2 2X 2X+2 2X+2
0 0 2X+2 2 0 2 2 2X 0 2 2X 2 2 2X+2 2X 0 0
0 0 0 2X 0 0 2X 0 2X 2X 2X 2X 0 2X 2X 0 2X
0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 0 2X 0 2X 0
generates a code of length 17 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+100x^14+285x^16+256x^17+312x^18+32x^20+36x^22+2x^24
The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 3.69 seconds.