The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+56x^12+8x^13+244x^14+216x^15+414x^16+1352x^17+876x^18+4568x^19+844x^20+4568x^21+980x^22+1352x^23+428x^24+216x^25+196x^26+8x^27+44x^28+8x^30+5x^32

The gray image is a code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 1.57 seconds.