The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+157x^74+205x^76+133x^78+9x^80+1x^82+1x^84+1x^86+2x^90+2x^94

The gray image is a code over GF(2) with n=608, k=9 and d=296.
This code was found by Heurico 1.16 in 10 seconds.