The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 1 1 1 X
0 X 0 0 0 X X+2 X 0 2 2 2 X X X+2 2 2 X+2 X+2 X+2
0 0 X 0 X X X 0 0 2 X+2 X 2 X+2 X+2 X X+2 X+2 X 0
0 0 0 X X 0 X X+2 2 X+2 X 0 X+2 2 X X X X+2 X 0
0 0 0 0 2 0 0 2 0 2 0 2 0 2 2 2 0 0 2 0
0 0 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 2 2 2
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+302x^16+192x^18+1072x^20+192x^22+272x^24+16x^28+1x^32
The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 8.33 seconds.