The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1 X+2  X  1  1  1  1  1  1
 0  1  0  0  1 X+1  1  1  X  1 X+2 X+1  1  2 X+1 X+3  2 X+1  2  1
 0  0  1  1  1  0 X+1  X X+1  1  X X+1  X  1 X+2  2 X+3  2 X+3  2
 0  0  0  X X+2  2  X  2 X+2  X  X  0 X+2 X+2  0 X+2  2 X+2  0  2
 0  0  0  0  2  0  2  2  0  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 16.

Homogenous weight enumerator: w(x)=1x^0+327x^16+136x^17+724x^18+352x^19+986x^20+432x^21+728x^22+96x^23+272x^24+8x^25+20x^26+14x^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 75.7 seconds.