The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  2  1  1  X  1  X  0  X  1
 0  X  0  0  0  0  0  0  0 X+2  X  X X+2  X  2 X+2  2  0  2  2
 0  0  X  0  0  0  X X+2  X  2 X+2  X X+2 X+2 X+2  0  X  0  2  2
 0  0  0  X  0  X  X  X  0 X+2  2 X+2  2  X X+2  X X+2  2  X X+2
 0  0  0  0  X  X  0  X X+2  X  2  X  X  0  0 X+2 X+2  X X+2  0
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  2  2  2
 0  0  0  0  0  0  2  0  2  0  2  2  0  2  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+52x^13+107x^14+202x^15+301x^16+572x^17+912x^18+1200x^19+1452x^20+1236x^21+934x^22+612x^23+282x^24+180x^25+88x^26+32x^27+12x^28+8x^29+7x^30+2x^31

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 0.783 seconds.