The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  X  1  1  1  1 X+2  1  1
 0  1  0  0  0  1  3 X+1  1  X  1  1  3  2 X+1  X  X  2 X+3
 0  0  1  0  1  1  2 X+2  1  3  3  2  1 X+3  X  2  1 X+2 X+1
 0  0  0  1  1  2  1  X  1 X+2 X+2 X+1  1 X+2  2  0 X+3 X+3  0
 0  0  0  0  X  0  0  2 X+2  2  0  2  2 X+2 X+2 X+2 X+2  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+312x^14+584x^15+1247x^16+1924x^17+2536x^18+3120x^19+2530x^20+2056x^21+1304x^22+488x^23+216x^24+20x^25+40x^26+6x^28

The gray image is a code over GF(2) with n=76, k=14 and d=28.
This code was found by Heurico 1.16 in 55.1 seconds.