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

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

Homogenous weight enumerator: w(x)=1x^0+15x^68+16x^69+45x^70+56x^71+73x^72+68x^73+272x^74+40x^75+259x^76+24x^77+53x^78+16x^79+20x^80+8x^81+1x^82+8x^83+10x^84+8x^85+10x^86+8x^87+6x^88+4x^89+2x^90+1x^138

The gray image is a code over GF(2) with n=300, k=10 and d=136.
This code was found by Heurico 1.16 in 0.37 seconds.