The generator matrix

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

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+91x^14+260x^15+687x^16+1048x^17+1911x^18+2764x^19+2804x^20+2832x^21+1924x^22+1052x^23+692x^24+216x^25+73x^26+20x^27+8x^28+1x^38

The gray image is a code over GF(2) with n=80, k=14 and d=28.
This code was found by Heurico 1.16 in 2.1 seconds.