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  0  X  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X 2X+2  1  1  X  1  1  X  1  1  X  0 2X  1  1 2X+2  X  2 2X  2  1
 0  X  0 3X+2  2 X+2 2X+2  X  0 X+2 2X X+2 3X  2  2  X  0 X+2  2 3X 2X 3X 2X 3X X+2  0  2  X  0 X+2  0 X+2  X  0  2  X 3X+2  X 3X 2X+2 2X 3X+2 X+2 3X+2 2X+2 2X  X  2 3X  2 3X+2 3X 3X 3X X+2  X 3X+2 3X+2 3X  0 2X  X  0 3X+2 3X+2  X  X  X  X  X  X  X  X  X 2X
 0  0 2X+2  0  2  0 2X  0  2  2 2X 2X+2 2X+2 2X+2  0  2  0 2X+2 2X 2X+2  2 2X  2  0  0 2X  0 2X  2  2  2  2 2X+2  0  0 2X 2X 2X+2  2 2X+2 2X+2 2X  0  2  2 2X  0  0 2X+2  0  2 2X  2  2  2 2X  2 2X  2 2X+2 2X+2  0  0 2X+2  2  2 2X  0  0 2X+2  0 2X  0 2X 2X
 0  0  0 2X+2  0 2X 2X  2  2  2  2  0  0  2 2X+2  2 2X 2X+2 2X+2 2X  0 2X+2 2X+2 2X  0 2X 2X+2 2X+2 2X 2X 2X+2 2X+2  2 2X+2  0 2X  2  0  0 2X  0 2X+2 2X+2  2 2X+2  0  0  2 2X+2 2X  0 2X 2X 2X+2  2 2X  0  0  2  2 2X 2X+2  0 2X 2X 2X+2  2 2X 2X  2  0 2X+2 2X+2 2X+2  0
 0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0  0 2X  0  0 2X  0  0  0 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+102x^69+184x^70+244x^71+262x^72+596x^73+357x^74+710x^75+308x^76+580x^77+260x^78+220x^79+125x^80+86x^81+13x^82+6x^83+4x^84+10x^85+15x^86+4x^87+3x^88+2x^89+2x^90+1x^94+1x^120

The gray image is a code over GF(2) with n=600, k=12 and d=276.
This code was found by Heurico 1.16 in 84.3 seconds.