The generator matrix

 1  0  0  0  0  1  1  1  1  X  X  1  0  1  0  2  0  1  2  1
 0  1  0  0  0  0  X  1 X+1  1  1 X+1  1  2  1  2  2  X  X  0
 0  0  1  0  0  0 X+1  X  1  3 X+1 X+3  2  3 X+3  X  1  X X+2 X+1
 0  0  0  1  0  1  1 X+1  2  1  1  2  X  1  2  1  3 X+2  1  0
 0  0  0  0  1  1  2  0  3 X+2  1  X X+1 X+1  0  1 X+2  3 X+3  0
 0  0  0  0  0  X  0  0  0  0 X+2  X  2  X  X  2 X+2  X  X  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+164x^13+778x^14+2100x^15+4525x^16+9096x^17+15737x^18+21400x^19+23618x^20+21276x^21+15351x^22+9412x^23+4862x^24+1904x^25+607x^26+176x^27+50x^28+8x^29+7x^30

The gray image is a code over GF(2) with n=80, k=17 and d=26.
This code was found by Heurico 1.13 in 35.1 seconds.