The generator matrix

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

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+194x^12+1070x^13+3188x^14+7028x^15+9665x^16+7340x^17+3096x^18+920x^19+234x^20+22x^21+4x^22+4x^23+2x^24

The gray image is a code over GF(2) with n=128, k=15 and d=48.
This code was found by Heurico 1.16 in 1.67 seconds.