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

generates a code of length 76 over Z4[X]/(X^2+2) 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 24.8 seconds.