The generator matrix

 1  0  1  1  1  2  1  1  0  0  1  1  1  0  1  1  2  1  1  1  2  1  1  0  1 X+2  1  0  1  1 X+2  1  1  1 X+2  1  1  1  1  1  1  X X+2  1  1 X+2 X+2  1  X  1 X+2  1  1  0  1  1  0  1  X  1  X X+2  1  1  1  1  X  1  1  1  1 X+2 X+2  1  X  1  1  1  2  1  1 X+2  1  1
 0  1  1  0  1  1  2 X+1  1  1  2 X+3  2  1  3  2  1 X+3 X+2  1  1  2 X+1  1  2  1  3  1 X+2 X+1  1 X+1  X X+2  1 X+3  1  0 X+1 X+2 X+1  1  1  0 X+2  1  1 X+3  1  2  1 X+1 X+2  1  X  3  1  3  1 X+2  1  1 X+2  X  2 X+2  1  X  0  2  3  1  1 X+3  1 X+3 X+3 X+1  1  2  1  1  2  2
 0  0  X  0  0  0  0  2 X+2  X X+2 X+2 X+2  2  0 X+2  X X+2  0 X+2  2  X  2 X+2  2  0  2 X+2 X+2  2 X+2  X  X  2 X+2 X+2  2  X  2 X+2 X+2  0 X+2 X+2  2  0 X+2  0  2  0  2 X+2  2  2 X+2  2 X+2  X  0 X+2  0  0  2  X  0  0  X  0  0 X+2  0 X+2  X X+2 X+2  2  0 X+2  2  0  0  2  0  2
 0  0  0  X  0  0  2  2  2  2  0  2  2 X+2  X X+2 X+2  X X+2 X+2  X  X  X X+2 X+2  2  0  0  0 X+2  X  X X+2  0  2  X  0  2  X X+2  2 X+2  0  0  2  X  2  X  2 X+2 X+2  0  2  0  0 X+2  0  2 X+2 X+2  X  0  2  0 X+2  0 X+2 X+2  2  X  0  2  X  X  X X+2  0  0 X+2 X+2  X X+2  X  0
 0  0  0  0  X X+2 X+2  2  X  0  0 X+2  X  X  X X+2  2  X  X  2  0  2  2  X X+2  2  2 X+2  X  X  0  0  X  X  2 X+2 X+2  0  X X+2  2  2  X X+2  2  0 X+2  0  0  0  X  X  0  X  0  0  0  X  X  0  2 X+2 X+2  X  2 X+2  0  2  0  0 X+2  X X+2  2  2  0  0  2  2 X+2  X X+2  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+30x^76+144x^77+241x^78+268x^79+308x^80+294x^81+266x^82+366x^83+427x^84+364x^85+261x^86+242x^87+239x^88+192x^89+196x^90+124x^91+28x^92+12x^93+20x^94+16x^95+18x^96+10x^97+6x^98+6x^99+2x^100+8x^101+2x^103+2x^104+1x^108+1x^110+1x^118

The gray image is a code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 1.41 seconds.