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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+142x^74+274x^75+472x^76+490x^77+663x^78+490x^79+781x^80+654x^81+751x^82+570x^83+622x^84+406x^85+507x^86+348x^87+371x^88+204x^89+177x^90+96x^91+77x^92+30x^93+26x^94+10x^95+11x^96+6x^97+6x^98+2x^99+1x^100+2x^101+2x^107

The gray image is a code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 4.9 seconds.