The generator matrix

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

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+24x^13+130x^14+264x^15+450x^16+1496x^17+1528x^18+3336x^19+1920x^20+3336x^21+1548x^22+1496x^23+440x^24+264x^25+120x^26+24x^27+2x^30+5x^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 36.5 seconds.