The generator matrix

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

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+180x^11+934x^12+2950x^13+7354x^14+9898x^15+7455x^16+2900x^17+884x^18+192x^19+10x^20+6x^21+2x^22+2x^23

The gray image is a code over GF(2) with n=120, k=15 and d=44.
This code was found by Heurico 1.16 in 1.53 seconds.