The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1 X+2  2  1  1  1  1  1  1 X+2
 0  1  1  0 X+3  1  X X+3  1  0 X+1  1  1  3 X+3  0  2  3  3  1
 0  0  X  0 X+2  2  0  0 X+2 X+2  X X+2  2  0  2  X  X  X X+2  0
 0  0  0  X  0  2 X+2  X  2 X+2  X  X X+2  2  2 X+2  0  X  X  2
 0  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  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+125x^16+128x^17+254x^18+384x^19+284x^20+384x^21+246x^22+128x^23+90x^24+10x^26+12x^28+2x^30

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 0.0602 seconds.