The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+84x^64+54x^66+36x^67+373x^68+196x^69+476x^70+408x^71+1032x^72+744x^73+1292x^74+1096x^75+1880x^76+1192x^77+1736x^78+1072x^79+1454x^80+752x^81+862x^82+436x^83+550x^84+180x^85+172x^86+24x^87+170x^88+8x^89+16x^90+56x^92+25x^96+5x^100+2x^104

The gray image is a code over GF(2) with n=308, k=14 and d=128.
This code was found by Heurico 1.16 in 19.3 seconds.