The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+96x^77+18x^78+42x^79+25x^80+32x^81+14x^82+12x^83+6x^84+6x^85+2x^87+2x^93

The gray image is a code over GF(2) with n=316, k=8 and d=154.
This code was found by Heurico 1.16 in 0.26 seconds.