The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  0  1  1  X  1  1  1
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  0  1 X+2 X+1  1  1 X+2  0
 0  0  X  0 X+2  0  X  2 X+2  X  0  X  0  2  0  2 X+2  X  2  0
 0  0  0  2  0  0  0  2  0  0  2  2  0  2  0  0  2  2  0  2
 0  0  0  0  2  0  0  0  2  2  2  0  2  2  0  2  2  0  0  0
 0  0  0  0  0  2  2  0  0  0  2  0  2  0  2  2  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+153x^16+64x^17+352x^18+192x^19+544x^20+192x^21+336x^22+64x^23+126x^24+16x^26+8x^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 0.0567 seconds.