The generator matrix

 1  0  1  1  1  0  1  1  2  1  1  X  0  2  X  X  1  0  1  0
 0  1  1  0 X+1  1 X+3  0  1  2  3  1  1  X  X  1  X  2 X+2  1
 0  0  X  0  0  0  0  X  X X+2 X+2  2  0  2  X  2  0  X X+2  0
 0  0  0  X  0 X+2 X+2  X  2  2  X  X  2 X+2  0  2  X  X X+2  0
 0  0  0  0  2  0  0  2  2  0  0  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  2
 0  0  0  0  0  0  2  0  0  2  0  0  2  2  2  2  2  2  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+82x^14+160x^15+433x^16+440x^17+1094x^18+944x^19+1865x^20+912x^21+1182x^22+480x^23+374x^24+120x^25+74x^26+16x^27+14x^28+1x^36

The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.67 seconds.