The generator matrix

 1  0  0  0  1  1  1 2X+2  1  1  1  1 3X 2X  1  1  1
 0  1  0  0  2 2X+1 2X+3  1 X+2 2X+2 X+3 X+1  1 3X 2X+1  1  0
 0  0  1  0  3  1  2  3  0 3X+1 X+2 2X+3 3X+3  1 3X+3 2X+3 3X+1
 0  0  0  1  1  2  3  3 X+1  X 2X+2 2X+3 2X+2 X+3 X+2 3X+3 2X+3

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+560x^13+2244x^14+6488x^15+14305x^16+18128x^17+14664x^18+6560x^19+1976x^20+512x^21+84x^22+8x^23+6x^24

The gray image is a code over GF(2) with n=136, k=16 and d=52.
This code was found by Heurico 1.16 in 6.44 seconds.