The generator matrix

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

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+193x^68+216x^69+698x^70+532x^71+1210x^72+796x^73+1474x^74+944x^75+1769x^76+1080x^77+1588x^78+1148x^79+1339x^80+716x^81+948x^82+472x^83+613x^84+200x^85+234x^86+40x^87+86x^88+42x^90+33x^92+8x^94+4x^96

The gray image is a code over GF(2) with n=308, k=14 and d=136.
This code was found by Heurico 1.16 in 16.1 seconds.