The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+76x^68+162x^69+195x^70+398x^71+413x^72+572x^73+677x^74+672x^75+727x^76+632x^77+730x^78+596x^79+626x^80+558x^81+370x^82+274x^83+154x^84+122x^85+55x^86+64x^87+41x^88+28x^89+19x^90+6x^91+6x^92+4x^93+6x^95+3x^96+2x^97+2x^98+1x^108

The gray image is a code over GF(2) with n=308, k=13 and d=136.
This code was found by Heurico 1.16 in 5.53 seconds.