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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+16x^77+8x^78+2x^80+4x^82+1x^88

The gray image is a code over GF(2) with n=304, k=5 and d=154.
This code was found by Heurico 1.16 in 0.206 seconds.