The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  2  1  0  1  X  X  X  X  1
 0  X  0  X  0  0  X X+2  0  X X+2  X  2  X  X  2 X+2  0  2  0
 0  0  X  X  0 X+2  X  0  X  X  0 X+2  X  2  X  X  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  0  2  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  0  2  2  0  0  0  0  2  2
 0  0  0  0  0  0  2  0  0  2  2  0  0  0  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  2  0  2  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  0  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+34x^12+50x^13+134x^14+200x^15+306x^16+592x^17+888x^18+1176x^19+1364x^20+1236x^21+900x^22+632x^23+312x^24+160x^25+120x^26+40x^27+26x^28+10x^29+6x^30+5x^32

The gray image is a code over GF(2) with n=80, k=13 and d=24.
This code was found by Heurico 1.16 in 0.558 seconds.