The generator matrix
1 0 1 1 1 0 1 2 1 1 0 1 1 1 X 2 1 X 1 1
0 1 1 0 1 1 0 1 X+1 X+1 1 0 0 2 2 1 X 1 1 0
0 0 X 0 0 0 0 X 0 X+2 X 2 X X 2 X+2 0 X+2 0 X+2
0 0 0 X 0 0 0 X+2 2 X+2 0 X+2 X+2 2 X+2 2 X+2 X X X
0 0 0 0 X X+2 X+2 X+2 2 0 X+2 X 2 X 0 2 2 X 0 2
0 0 0 0 0 2 0 2 2 2 0 0 0 0 2 2 2 0 0 0
0 0 0 0 0 0 2 0 0 0 0 0 2 2 2 2 0 2 2 0
generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.
Homogenous weight enumerator: w(x)=1x^0+48x^13+157x^14+234x^15+547x^16+1098x^17+1911x^18+2626x^19+2961x^20+2890x^21+1917x^22+1022x^23+559x^24+238x^25+109x^26+22x^27+27x^28+14x^29+2x^30+1x^32
The gray image is a code over GF(2) with n=80, k=14 and d=26.
This code was found by Heurico 1.16 in 2.06 seconds.