The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+66x^67+337x^68+516x^69+940x^70+852x^71+1205x^72+1030x^73+1481x^74+1214x^75+1494x^76+1112x^77+1402x^78+1084x^79+1155x^80+672x^81+683x^82+374x^83+329x^84+172x^85+149x^86+56x^87+15x^88+18x^89+16x^90+2x^91+8x^92+1x^94

The gray image is a code over GF(2) with n=304, k=14 and d=134.
This code was found by Heurico 1.16 in 14.5 seconds.