The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+55x^76+236x^77+243x^78+514x^79+275x^80+446x^81+295x^82+448x^83+221x^84+316x^85+171x^86+260x^87+108x^88+150x^89+86x^90+96x^91+27x^92+62x^93+25x^94+26x^95+16x^96+4x^97+11x^98+1x^100+2x^101+1x^102

The gray image is a code over GF(2) with n=332, k=12 and d=152.
This code was found by Heurico 1.16 in 1.21 seconds.