The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+94x^13+266x^14+370x^15+635x^16+340x^17+236x^18+76x^19+4x^20+14x^21+10x^22+2x^23

The gray image is a code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.063 seconds.