The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+50x^74+156x^75+62x^76+68x^77+23x^78+56x^79+38x^80+20x^81+5x^82+20x^83+9x^84+1x^88+1x^90+1x^94+1x^100

The gray image is a code over GF(2) with n=308, k=9 and d=148.
This code was found by Heurico 1.16 in 0.158 seconds.