The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+28x^80+2x^84+1x^88

The gray image is a code over GF(2) with n=312, k=5 and d=160.
This code was found by Heurico 1.16 in 0.228 seconds.