The generator matrix

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

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+101x^76+340x^77+409x^78+626x^79+531x^80+780x^81+547x^82+744x^83+567x^84+600x^85+490x^86+620x^87+419x^88+430x^89+260x^90+236x^91+154x^92+166x^93+81x^94+38x^95+17x^96+16x^97+5x^98+6x^99+2x^100+2x^101+2x^105+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 1.13 in 1.8 seconds.