The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2 X+1  1  3  3  3 X+1 X+1 X+3 X+1  0
 0  0  2  0  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  0
 0  0  0  2  0  0  0  2  0  2  2  0  0  2  0  2  2  0  2  0
 0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  0  0
 0  0  0  0  0  2  0  2  2  0  2  0  0  0  2  0  2  2  0  0
 0  0  0  0  0  0  2  2  0  0  2  2  2  2  2  0  2  2  2  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+11x^14+40x^15+47x^16+168x^17+315x^18+176x^19+549x^20+176x^21+301x^22+168x^23+35x^24+40x^25+9x^26+7x^28+4x^30+1x^32

The gray image is a code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.0368 seconds.