The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+38x^8+69x^12+128x^14+1536x^15+205x^16+58x^20+12x^24+1x^28

The gray image is a code over GF(2) with n=120, k=11 and d=32.
This code was found by Heurico 1.16 in 0.016 seconds.