The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+22x^13+61x^14+112x^15+136x^16+120x^17+579x^18+240x^19+1522x^20+276x^21+584x^22+144x^23+126x^24+88x^25+52x^26+16x^27+6x^28+6x^29+3x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=80, k=12 and d=26.
This code was found by Heurico 1.16 in 3.09 seconds.