The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  0  1  1  1  1  1  1  1  0  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  1 X+1  0 X+2  0 X+2  3  0  1  0
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0
 0  0  0  2  0  0  0  0  0  2  0  0  2  2  0  0  2  2  0  2
 0  0  0  0  2  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  2  2  0  0  0  2  2  2  0  0  0  2
 0  0  0  0  0  0  2  0  2  0  2  0  2  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  2  2  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+60x^14+197x^16+192x^17+568x^18+576x^19+889x^20+576x^21+608x^22+192x^23+186x^24+40x^26+6x^28+4x^30+1x^36

The gray image is a code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 0.16 seconds.