The generator matrix

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

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+24x^12+8x^13+54x^14+56x^15+121x^16+424x^17+208x^18+1048x^19+208x^20+1048x^21+201x^22+424x^23+142x^24+56x^25+40x^26+8x^27+16x^28+8x^30+1x^38

The gray image is a code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.133 seconds.