The generator matrix

 1  0  1  1  1 X+2  1  2  1  1  X  1  0  1  1  1 X+2  1  1  1
 0  1  1 X+2 X+3  1  2  1 X+1  X  1  3  1  X  2  3  1 X+1  X  2
 0  0  X  0 X+2  2  X  X  0 X+2 X+2  0  2  X  X  2  2  0  X X+2
 0  0  0  2  0  2  0  2  2  2  0  0  2  0  2  0  0  2  2  2
 0  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  2  0  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+50x^16+64x^17+136x^18+192x^19+157x^20+192x^21+112x^22+64x^23+41x^24+8x^26+7x^28

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.014 seconds.