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

generates a code of length 75 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+82x^65+186x^66+214x^67+286x^68+330x^69+429x^70+470x^71+559x^72+694x^73+632x^74+716x^75+625x^76+574x^77+558x^78+372x^79+382x^80+308x^81+188x^82+154x^83+121x^84+104x^85+70x^86+46x^87+42x^88+20x^89+14x^90+12x^91+2x^94+1x^102

The gray image is a code over GF(2) with n=300, k=13 and d=130.
This code was found by Heurico 1.16 in 59.9 seconds.