The generator matrix

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

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+105x^16+124x^17+368x^18+264x^19+374x^20+256x^21+304x^22+120x^23+106x^24+4x^25+16x^26+6x^28

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0387 seconds.