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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+21x^76+108x^77+20x^78+72x^79+9x^80+12x^81+9x^82+1x^86+1x^92+1x^98+1x^102

The gray image is a code over GF(2) with n=312, k=8 and d=152.
This code was found by Heurico 1.16 in 0.233 seconds.