The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  2  X  1  2  X  1  1  1
 0  X  0  0  0  0  0  0  0  X  X  X  2 X+2  X  0  X  2  X  0
 0  0  X  0  0  0  X X+2  X  X  X X+2  X X+2  2  X  0  2  0  0
 0  0  0  X  0  X  X X+2  0  0  0 X+2  2  2  2 X+2 X+2 X+2  2  0
 0  0  0  0  X  X  0 X+2  X  0  2 X+2  X  X  X  0  2  X  X  0
 0  0  0  0  0  2  0  0  2  0  0  0  2  0  2  2  2  2  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  2  2  2  2  0
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  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+86x^12+88x^13+277x^14+332x^15+555x^16+930x^17+1759x^18+2722x^19+2806x^20+2754x^21+1812x^22+986x^23+564x^24+310x^25+232x^26+54x^27+84x^28+14x^29+15x^30+2x^31+1x^34

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 2.29 seconds.