The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+54x^13+96x^14+242x^15+429x^16+444x^17+416x^18+228x^19+48x^20+46x^21+32x^22+10x^23+2x^24

The gray image is a code over GF(2) with n=136, k=11 and d=52.
This code was found by Heurico 1.16 in 0.047 seconds.