The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+36x^10+72x^11+129x^12+342x^13+603x^14+1720x^15+605x^16+372x^17+122x^18+48x^19+33x^20+6x^21+7x^22

The gray image is a code over GF(2) with n=120, k=12 and d=40.
This code was found by Heurico 1.16 in 0.047 seconds.