The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  1  1
 0 2X  0  0  0  0  0  0 2X  0 2X 2X  0 2X  0
 0  0 2X  0  0  0  0  0 2X 2X 2X  0  0 2X 2X
 0  0  0 2X  0  0  0 2X  0 2X  0 2X  0 2X 2X
 0  0  0  0 2X  0  0 2X  0  0 2X 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X  0 2X  0 2X  0 2X
 0  0  0  0  0  0 2X 2X 2X  0  0 2X  0  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+17x^10+28x^12+32x^13+20x^14+832x^15+21x^16+32x^17+22x^18+12x^20+4x^22+2x^24+1x^26

The gray image is a code over GF(2) with n=120, k=10 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.