The generator matrix

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

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+77x^74+290x^75+432x^76+664x^77+570x^78+712x^79+556x^80+862x^81+530x^82+612x^83+463x^84+540x^85+390x^86+476x^87+312x^88+238x^89+165x^90+164x^91+55x^92+32x^93+20x^94+16x^95+2x^96+8x^98+2x^99+2x^100+1x^104

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 3.66 seconds.