The generator matrix

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

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+60x^11+546x^12+1400x^13+3564x^14+5264x^15+3551x^16+1416x^17+496x^18+52x^19+30x^20+4x^22

The gray image is a code over GF(2) with n=120, k=14 and d=44.
This code was found by Heurico 1.16 in 0.391 seconds.