The generator matrix

 1  0  0  0  1  1  1  2  1  1 X+2 X+2 X+2  1  1  X  1  1  1
 0  1  0  0  0  1  1  1  2 X+2  X  1  2 X+3  X  1  3  2  2
 0  0  1  0  1  1  0  3  2  3  1 X+1  1 X+1  X  0 X+3 X+2  0
 0  0  0  1  1  2  3  1 X+1  X X+3  0  X X+3  3 X+1 X+3 X+2  X
 0  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  0

generates a code of length 19 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+83x^14+384x^15+597x^16+1046x^17+1245x^18+1458x^19+1244x^20+1156x^21+573x^22+268x^23+90x^24+38x^25+3x^26+2x^27+4x^28

The gray image is a code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.13 in 0.208 seconds.