The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+110x^76+246x^77+489x^78+524x^79+725x^80+612x^81+763x^82+532x^83+693x^84+520x^85+663x^86+450x^87+500x^88+336x^89+382x^90+188x^91+142x^92+116x^93+88x^94+26x^95+32x^96+18x^97+14x^98+6x^99+3x^100+6x^101+2x^104+2x^105+1x^106+2x^107

The gray image is a code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 5.09 seconds.