The generator matrix

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

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+8x^13+70x^14+212x^15+216x^16+568x^17+978x^18+1332x^19+1554x^20+1080x^21+982x^22+732x^23+270x^24+136x^25+6x^26+28x^27+6x^28+12x^30+1x^32

The gray image is a code over GF(2) with n=80, k=13 and d=26.
This code was found by Heurico 1.16 in 84.8 seconds.