The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+100x^12+48x^14+64x^15+634x^16+320x^17+464x^18+1664x^19+1592x^20+1664x^21+464x^22+320x^23+664x^24+64x^25+48x^26+68x^28+13x^32

The gray image is a code over GF(2) with n=80, k=13 and d=24.
This code was found by Heurico 1.16 in 0.523 seconds.