The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  2  1  1  1  1  1  X  X
 0  X  0  X  0  0  X X+2  2  0  2  X  X X+2  2  X  X  X  X  X
 0  0  X  X  0 X+2  X  2  0  0  X X+2 X+2  2 X+2  0  X X+2  X X+2
 0  0  0  2  0  0  2  0  0  2  2  2  0  2  0  0  0  2  2  0
 0  0  0  0  2  0  0  0  2  2  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  0  2  2  2  2  0  0  0  2  0  2  2  2  2  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+94x^16+32x^17+144x^18+224x^19+64x^20+224x^21+96x^22+32x^23+96x^24+16x^26+1x^32

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 0.019 seconds.