The generator matrix

 1  1  1  1  1  X  0  1  1  1  X  0  X  X  1
 0  X  2 3X+2  0 3X+2  X 3X+2  2 3X 3X  X 3X+2 3X+2  0
 0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0  0
 0  0  0 2X  0  0 2X 2X 2X 2X  0  0  0  0  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0
 0  0  0  0  0 2X 2X 2X 2X  0  0 2X 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+10x^10+20x^11+90x^12+256x^13+288x^14+728x^15+281x^16+256x^17+82x^18+20x^19+10x^20+4x^22+2x^24

The gray image is a code over GF(2) with n=120, k=11 and d=40.
This code was found by Heurico 1.16 in 0.015 seconds.