The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+211x^16+352x^17+664x^18+500x^19+568x^20+672x^21+664x^22+232x^23+160x^24+32x^25+32x^26+4x^27+4x^28

The gray image is a code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 0.188 seconds.