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

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+134x^70+145x^72+96x^73+532x^74+320x^75+456x^76+96x^77+166x^78+37x^80+50x^82+12x^86+2x^90+1x^136

The gray image is a code over GF(2) with n=600, k=11 and d=280.
This code was found by Heurico 1.16 in 107 seconds.