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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+80x^75+26x^76+60x^77+12x^78+40x^79+19x^80+4x^81+4x^82+6x^83+2x^84+2x^91

The gray image is a code over GF(2) with n=308, k=8 and d=150.
This code was found by Heurico 1.16 in 0.224 seconds.