The generator matrix

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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+116x^68+584x^69+1576x^70+2014x^71+3432x^72+2932x^73+3851x^74+3968x^75+4362x^76+3016x^77+2878x^78+1556x^79+1211x^80+608x^81+349x^82+120x^83+111x^84+24x^85+12x^86+22x^87+14x^88+4x^89+6x^90+1x^92

The gray image is a code over GF(2) with n=600, k=15 and d=272.
This code was found by Heurico 1.16 in 11.6 seconds.