The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  2  0  X  1  1
 0  X  0  0  0  0  0  0  0  X X+2  X  2  X  2  X  2 X+2  X  0
 0  0  X  0  0  0  X X+2  X  X  X  0  X  2  X  X  X  0  X  X
 0  0  0  X  0  X  X  X  2  0  0  2  X  0  X  2 X+2  2  0  X
 0  0  0  0  X  X  2 X+2 X+2  0  X  X  X X+2 X+2  2 X+2  0  2  0
 0  0  0  0  0  2  2  2  2  2  0  0  0  2  0  2  2  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+100x^14+8x^15+310x^16+104x^17+688x^18+400x^19+866x^20+400x^21+724x^22+104x^23+278x^24+8x^25+88x^26+14x^28+3x^32

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 0.208 seconds.