The generator matrix

 1  1  1  1  1  1  1  X  1  1  X  1  X X^2  X  X X^2  2  0
 0  2  0  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  2

generates a code of length 19 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+20x^19+5x^20+4x^21+2x^22

The gray image is a code over GF(2) with n=152, k=5 and d=76.
This code was found by Heurico 1.16 in -3.24e-008 seconds.