The generator matrix

 1  1  1  1  1  1  1  1  1  X  2  X  1  1  1  1  1
 0 2X+2  0 2X+2  0 2X+2  0  2 2X 2X+2 2X+2 2X+2 2X+2  0  0 2X  0
 0  0 2X  0  0  0  0  0 2X  0 2X 2X  0  0 2X 2X  0
 0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X  0  0
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0
 0  0  0  0  0 2X  0 2X  0 2X 2X  0  0 2X  0 2X  0
 0  0  0  0  0  0 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X

generates a code of length 17 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+58x^12+56x^14+64x^15+537x^16+640x^17+496x^18+64x^19+92x^20+24x^22+14x^24+2x^28

The gray image is a code over GF(2) with n=136, k=11 and d=48.
This code was found by Heurico 1.16 in 0.015 seconds.