The generator matrix

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

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+21x^10+18x^11+48x^12+82x^13+574x^14+572x^15+571x^16+76x^17+38x^18+18x^19+20x^20+2x^21+6x^22+1x^26

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.