The generator matrix

 1  0  0  1  1  1 2X+2 2X  0  2  1  1  1  1 3X  1  1 3X+2  1  1 3X  1 X+2  X  1  1  1 3X+2  1  0 2X 3X  1  1  1  1  1  1  1 3X 3X  1  X 2X  1  1  2  1  2 2X+2  1  1  1  1  1  1  2  1  2 3X  1 2X X+2  1  1  1  1  0  1  1  1  1  1  0  1
 0  1  0  0  3 2X+3  1 X+2  1  1 2X  0  3  3 3X X+2 X+3  1 X+1  X  1 3X+1 2X+2  1 X+2 3X X+3  1 2X+1  1  1 X+2  2 3X+3  2 2X+1  X 2X+1 2X  1  1 3X+1  1  2  X 3X  1 3X+1  1  1 3X+3 2X 2X  1 2X 3X+2 2X+2 X+1  1 2X+2 X+2  1  1  X 3X 2X X+3  0 2X+1 X+2  2 2X+1 3X+1  2  0
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1 X+2  3 2X+1  X  1  3  1 3X+2 3X X+2 X+3 3X+1  1 2X+1 3X+3  0  2 2X 2X+2 X+1 X+2  1 2X+3 3X+1 2X X+3 X+3  X X+2 2X+1 3X+2  1  X  1 2X+1 3X X+3 2X+3 2X+3  2 3X+2 3X+2 3X+3 X+2 2X+3 3X  1 X+2  1  1 2X+1  3  0  3 2X+2 2X+3 3X+1  1  1 X+2  0 2X 3X+3  1 2X
 0  0  0  2  2  0  2 2X+2  2 2X 2X+2 2X 2X 2X+2  0  0  0 2X  2  2  0 2X+2 2X+2  2  2  0 2X  2  2 2X+2 2X 2X+2  2  0 2X  0 2X  2  0 2X 2X+2  2  0 2X 2X+2  0 2X 2X+2  2  2  0  2 2X 2X  0  2  2 2X+2  0  0  2 2X+2 2X  0 2X+2  2 2X+2  2 2X+2 2X  2 2X  0 2X+2 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+118x^69+737x^70+1292x^71+1386x^72+1850x^73+2283x^74+1896x^75+1811x^76+1614x^77+1394x^78+896x^79+454x^80+282x^81+199x^82+78x^83+38x^84+20x^85+11x^86+10x^87+5x^88+4x^89+2x^91+1x^92+2x^95

The gray image is a code over GF(2) with n=600, k=14 and d=276.
This code was found by Heurico 1.16 in 3.45 seconds.