The generator matrix

 1  0  0  1  1  1  2  0  1 X+2  1  1 X+2  1  1  0  X X+2  2  2
 0  1  0  0  3  3  1 X+2  2  1 X+2 X+3  1 X+1  0  1  1  1  1  1
 0  0  1 X+1 X+3  2 X+3  1  X  0 X+1  1  3  2  X X+3 X+1  X  1  1
 0  0  0  2  2  0  2  2  2  2  0  0  0  2  0  0  2  2  0  2

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+128x^17+138x^18+224x^19+131x^20+160x^21+92x^22+96x^23+11x^24+32x^25+10x^26+1x^28

The gray image is a code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.16 in 0.2 seconds.