The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  1
 0  X  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  0 X+2  2  2  X  2  0  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  0  2  2  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  0  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+21x^16+104x^18+25x^20+80x^22+10x^24+8x^26+6x^28+1x^36

The gray image is a code over GF(2) with n=80, k=8 and d=32.
This code was found by Heurico 1.16 in 0.00351 seconds.