The generator matrix

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

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+139x^18+210x^19+138x^20+196x^21+66x^22+72x^23+37x^24+28x^25+3x^26+6x^27

The gray image is a code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.11 in 5.03 seconds.