The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+124x^69+259x^70+394x^71+586x^72+580x^73+621x^74+682x^75+725x^76+714x^77+546x^78+666x^79+572x^80+370x^81+451x^82+302x^83+172x^84+166x^85+98x^86+60x^87+42x^88+26x^89+8x^90+8x^91+11x^92+4x^93+1x^94+3x^96

The gray image is a code over GF(2) with n=308, k=13 and d=138.
This code was found by Heurico 1.16 in 4.53 seconds.