The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+254x^76+276x^77+488x^78+316x^79+531x^80+276x^81+378x^82+244x^83+290x^84+136x^85+238x^86+136x^87+164x^88+92x^89+94x^90+28x^91+64x^92+20x^93+50x^94+12x^95+8x^96

The gray image is a code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 1.05 seconds.