The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X  X  1  X  1  1  1  1  X
 0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  2  2
 0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  2  2  0  0  0
 0  0  0  2  0  2  0  2  2  0  0  0  0  2  2  0  2  2  2  2
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  0  2  0  0  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+10x^17+10x^18+74x^20+20x^21+5x^22+5x^24+2x^25+1x^30

The gray image is a code over GF(2) with n=80, k=7 and d=34.
This code was found by Heurico 1.16 in 0.0117 seconds.