The generator matrix

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

generates a code of length 16 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+105x^12+568x^13+1376x^14+3710x^15+4879x^16+3748x^17+1312x^18+544x^19+125x^20+4x^21+8x^22+2x^23+2x^24

The gray image is a code over GF(2) with n=128, k=14 and d=48.
This code was found by Heurico 1.16 in 0.422 seconds.