The generator matrix

 1  0  1  1  1  0  1  2  1  1  0  1  1  1  X  2  1  X  1  1
 0  1  1  0  1  1  0  1 X+1 X+1  1  0  0  2  2  1  X  1  1  0
 0  0  X  0  0  0  0  X  0 X+2  X  2  X  X  2 X+2  0 X+2  0 X+2
 0  0  0  X  0  0  0 X+2  2 X+2  0 X+2 X+2  2 X+2  2 X+2  X  X  X
 0  0  0  0  X X+2 X+2 X+2  2  0 X+2  X  2  X  0  2  2  X  0  2
 0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  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+48x^13+157x^14+234x^15+547x^16+1098x^17+1911x^18+2626x^19+2961x^20+2890x^21+1917x^22+1022x^23+559x^24+238x^25+109x^26+22x^27+27x^28+14x^29+2x^30+1x^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 2.06 seconds.