The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+366x^11+1882x^12+6096x^13+14112x^14+20406x^15+14551x^16+6000x^17+1664x^18+410x^19+46x^20+2x^23

The gray image is a code over GF(2) with n=120, k=16 and d=44.
This code was found by Heurico 1.16 in 5.61 seconds.