The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+30x^78+168x^79+234x^80+240x^81+264x^82+180x^83+166x^84+146x^85+98x^86+110x^87+91x^88+88x^89+60x^90+32x^91+33x^92+34x^93+20x^94+22x^95+18x^96+4x^97+8x^98+1x^100

The gray image is a code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.11 in 0.424 seconds.