The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+88x^69+631x^70+1416x^71+1297x^72+2290x^73+1806x^74+2330x^75+1497x^76+1718x^77+1115x^78+1000x^79+486x^80+396x^81+147x^82+62x^83+36x^84+34x^85+14x^86+8x^87+2x^88+2x^89+7x^90+1x^92

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 3.49 seconds.