The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+224x^74+144x^76+80x^78+25x^80+32x^82+4x^84+1x^88+1x^104

The gray image is a code over GF(2) with n=304, k=9 and d=148.
This code was found by Heurico 1.16 in 7.21 seconds.