The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1 3X+2  X  X  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1 2X+1 3X  1  0  0  0
 0  0 2X  0  0  0 2X 2X  0  0 2X  0  0 2X  0
 0  0  0 2X  0  0 2X  0  0 2X 2X 2X  0 2X  0
 0  0  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0  0
 0  0  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X  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+19x^10+54x^11+83x^12+322x^13+1185x^14+788x^15+1174x^16+316x^17+69x^18+54x^19+21x^20+2x^21+7x^22+1x^24

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 0.015 seconds.