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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+54x^74+128x^75+167x^76+128x^77+20x^78+6x^80+1x^84+4x^86+1x^88+2x^106

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 0.937 seconds.