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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+76x^75+140x^76+16x^77+11x^78+3x^80+4x^82+4x^91+1x^94

The gray image is a code over GF(2) with n=608, k=8 and d=300.
This code was found by Heurico 1.16 in 24.7 seconds.