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  1  1  1  1  1 2X  1  1  0  X 2X+2  X  0 2X+2  X  X  X  X
 0  X 2X+2 X+2  0 X+2 2X+2 3X X+2  0 3X 2X+2 3X 2X  2 X+2 3X+2  0 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X+2 3X 3X+2  0  X 2X+2 2X  2 X+2 3X+2 2X 3X  X  2 3X+2  X X+2  0 2X 3X  0 2X+2 2X+2  2 X+2 X+2 3X+2 3X+2 2X+2  2  2  0 2X 2X 3X 3X 2X  X  X  X X+2  X 3X  X  X X+2  0 2X+2  0
 0  0 2X  0  0  0 2X  0 2X  0 2X 2X 2X  0 2X  0 2X  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0 2X  0
 0  0  0 2X  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0 2X 2X  0 2X  0 2X  0
 0  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0  0  0 2X 2X  0  0 2X 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0  0  0  0 2X  0  0  0  0 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X  0  0  0 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+60x^70+96x^71+192x^72+288x^73+360x^74+224x^75+376x^76+32x^77+188x^78+64x^79+70x^80+64x^81+32x^82+1x^128

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 0.515 seconds.