The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+174x^16+672x^20+176x^24+1x^32

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 6.69 seconds.