The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+166x^76+32x^78+53x^80+1x^84+2x^88+1x^100

The gray image is a code over GF(2) with n=308, k=8 and d=152.
This code was found by Heurico 1.16 in 0.238 seconds.