The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  0  0  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0

generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+140x^8+448x^12+7014x^16+448x^20+140x^24+1x^32

The gray image is a code over GF(2) with n=64, k=13 and d=16.
This code was found by Heurico 1.16 in 18.1 seconds.