The generator matrix
1 1 1 1 1 1 1 1 X X 1 X 2 1 1 1 1 1 1 1
0 X 0 0 0 X X+2 X 2 0 0 X+2 X 0 X X 0 2 0 0
0 0 X 0 X X X+2 0 0 X 0 X 0 X+2 X+2 2 2 2 0 0
0 0 0 X X 0 X+2 X X X 2 X X 2 2 2 2 2 2 0
0 0 0 0 2 0 0 0 0 2 2 2 2 0 2 2 0 2 2 0
0 0 0 0 0 2 0 0 2 2 2 0 0 2 2 0 2 2 0 0
0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 0 0 2 0 0
0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 0 2 0 0
generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+72x^12+190x^14+474x^16+256x^17+804x^18+1792x^19+964x^20+1792x^21+896x^22+256x^23+460x^24+156x^26+68x^28+2x^30+9x^32
The gray image is a code over GF(2) with n=80, k=13 and d=24.
This code was found by Heurico 1.16 in 0.603 seconds.