The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+458x^14+932x^15+2765x^16+4000x^17+8642x^18+9316x^19+13000x^20+9568x^21+8898x^22+4012x^23+2690x^24+768x^25+366x^26+76x^27+40x^28+4x^30

The gray image is a code over GF(2) with n=80, k=16 and d=28.
This code was found by Heurico 1.13 in 10.6 seconds.