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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+36x^73+135x^74+80x^75+80x^76+44x^77+79x^78+12x^79+4x^80+16x^81+16x^82+4x^83+1x^84+1x^88+1x^90+1x^94+1x^100

The gray image is a code over GF(2) with n=304, k=9 and d=146.
This code was found by Heurico 1.13 in 0.125 seconds.