The generator matrix

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

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+314x^14+560x^15+1340x^16+1780x^17+2668x^18+2928x^19+2783x^20+1944x^21+1284x^22+448x^23+287x^24+20x^25+20x^26+5x^28+2x^30

The gray image is a code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.13 in 7.12 seconds.